OPINION OF THE COURT
Defendants Peter Chan and Billy Chin appeal from orders of the Appellate Division, First Department, which affirmed separate judgments of the Supreme Court, New York County, convicting them of attempted murder in the second degree, upon a jury verdict, and imposing sentence. The pivotal issue is whether they were denied their constitutional right to confront an adverse witness, the victim of the crime, when the witness invoked his privilege against self-incriminatian on cross-examination. We conclude that there was no infringement of the right to confrontation, and, finding no merit to any of the other contentions raised, affirm the orders of the Appellate Division.
I
On December 23, 1980, an attempt was made to shoot and kill Robert Hu. The shooting was part of an ongoing battle between rival street gangs for control of the extortion and gambling protection rackets in the Chinatown section of Manhattan. Hu was the leader of the Ghost Shadows gang which some two years earlier had expelled Nickie Louie from its ranks. Louie, a codefendant acquitted at trial, formed a new gang, the White Tigers, recruiting defendants Chan and Chin and others, with the aim of compelling Hu to relinquish the "territory” to them.
Hu and Louie met at a coffee shop at about 6:45 p.m. Police officers were present conducting surveillance. In essence, Louie demanded that Hu turn over control of the Mott Street rackets to his gang. Hu refused and left the restaurant, police officers following behind.
Outside, an officer observed Chin crouched behind a parked van, holding a gun. Chin turned toward a detective and pointed the gun at him. Officers directed Chin to drop the weapon, but Chin stared at them and fled south on Mott Street. As an officer gave chase, two shots rang out.
*26In the meantime, two other officers exited the coffee shop, and were directed by a passerby in the opposite direction, north towards Canal Street. Both ran as far as Canal Street, and, finding nothing of interest, returned down Mott Street. When they reached the van parked near the coffee shop, Hu yelled "Under the van. Under the van.” An officer recovered a gun from underneath the van’s left rear tire. By this time Chin, who had been shot in the hand, had been apprehended.
Hu had an extensive criminal record and had an extortion charge pending against him in Maryland. He was detained in jail as a material witness during trial. All parties were advised by Hu’s attorney that Hu would assert his privilege against self-incrimination on all matters for which he did not receive complete immunity. The People stated that their direct examination would be limited to those questions asked in the Grand Jury for which Hu had already received immunity (CPL 190.40). Defense counsel protested that their cross-examination would be impermissibly curtailed and sought to preclude Hu from taking the stand. That application was denied.
On direct examination, Hu was questioned about the events which occurred subsequent to his departure from the coffee shop. As to each question, he asserted his privilege against self-incrimination. The prosecutor then requested that immunity be conferred, the trial court did so, and Hu responded.
Hu testified that while he was standing in front of the coffee shop, he saw Chan and Chin approach him from across the street. Chan said, "Don’t go. I have something to talk to you [sic]. ” When Chan and Chin tried to fire weapons, Hu ran to an unmarked police car and pounded on the hood. A voice, which Hu thought was Nickie Louie’s, called out "shoot, shoot, shoot.” Hu threw himself to the ground, hearing a total of three shots. Chan dropped his weapon and kicked it under the van.
At the outset of cross-examination, Hu was asked if he was a member of the Ghost Shadows on December 23, 1980, and if he possessed a gun within three months of that date. Hu refused to answer, and the prosecutor declined to request that immunity be conferred by the court, instead offering a stipulation to the effect that the questions would be answered in the affirmative. The stipulation was declined. In addition, the prosecutor urged that any cross-examination concerning the history of Chinese youth gangs would be collateral, a contention accepted by the trial court.
*27Defendants were able to cross-examine Hu about all matters covered in his direct examination. More specifically, they were able to inquire about Hu’s acquaintance with the defendants, his knowledge of weapons, whether he carried a weapon on the day of the shooting, his observations during the shooting, including the fact that he never saw who fired the shots, the circumstances of his arrest after the shooting, and his inconsistent statements to the police and to the Grand Jury.
During and after cross-examination, defense counsel sought to strike Hu’s direct testimony, claiming that certain areas of legitimate inquiry were foreclosed. These areas included Hu’s fear of prosecution for the murder of a rival gang member who was present at the scene of the shooting; Hu’s membership in a rival gang; the reasons for Hu’s presence on Mott Street on the evening of the shooting; the conversation at the coffee shop; Hu’s means of earning a living; whether the People had made any threats or promises to induce Hu to testify; and whether Hu had been involved in the shooting of defendant Chin six months after the crime.
The prosecutor responded that Hu’s testimony on these points would be "cumulative” and "collateral” as they were not the subject of his direct examinations. At the completion of cross-examination, the prosecutor offered a series of stipulations, including those providing that Hu was "a member and leader of the Ghost Shadows,” that he "earns his living through both legal and illegal means,” and that "he has an interest in seeing that these defendants are convicted.” All the tendered stipulations were rejected by defense counsel, and the motions to strike Hu’s testimony were denied.
Defendants contend that they were unable to effectively cross-examine Hu, and that their motion to strike his direct testimony should have been granted.
II
It is, of course, basic that a defendant in a criminal cause has a constitutional right to confront witnesses against him through cross-examination (US Const 6th Amend; NY Const, art I, § 6; Davis v Alaska, 415 US 308, 315-316; People v Gissendanner, 48 NY2d 543, 548; see also, Civil Rights Law § 12), a process Wigmore describes as "beyond any doubt the greatest legal engine ever invented for the discovery of truth” (5 Wigmore, Evidence § 1367, at 32 [Chadbourn rev 1974]). As the Supreme Court has observed, "Cross-examination is the *28principal means by which the believability of a witness and the truth of his testimony are tested” (Davis v Alaska, supra, at p 316).
Although a cross-examiner may delve deep in order to attack credibility and present an alternate view of the facts, such inquiry is not open-ended. A witness may, if appropriate, invoke the constitutional shield of self-incrimination (Alford v United States, 282 US 687, 694; People v Farruggia, 77 AD2d 447, 452).1 Refusal to answer the cross-examiner’s questions may so distort the fact-finding process that some or all of the direct testimony must be struck, lest the defendant be deprived of a fair trial (see, People v Schneider, 36 NY2d 708, revg on dissent of Justice Hopkins at 44 AD2d 845; People v Acomb, 87 AD2d 1; People v Farruggia, supra).
Decisional law generally distinguishes between invoking the privilege on matters that are collateral to the direct examination, which does not require the striking of direct testimony (see, e.g., People v Allen, 50 NY2d 898, affg 67 AD2d 558; People v Codrington, 109 AD2d 891; People v Jones, 99 AD2d 471, 472, overruled on another issue in People v Magazine, 106 AD2d 473; Dunbar v Harris, 612 F2d 690), and invoking the privilege on matters directly related to the direct examination, which entitles the defendant to have the direct testimony stricken (see, e.g., People v Schneider, 36 NY2d 708, supra; People v Acomb, supra; People v Farruggia, 77 AD2d 447, supra; United States v Newman, 490 F2d 139).2 The distinction between matters which are "collateral” and those which are "direct” is not precise or easy to draw (United States v Seifert, 648 F2d 557, 561), and these terms are simply guidelines. In each case, "the ultimate question must be whether the defendant’s inability to test the accuracy of the witness’ direct examination has been such as to create a substantial risk of prejudice” (McCormick, Evidence § 140, at 347 [3d ed]; see generally, Ann., 55 ALR Fed 742).
If the cross-examiner seeks to explore more than mere general credibility, as, for example, to establish bias or interest, the subject of inquiry is not collateral (see, Dunbar v *29Harris, 612 F2d 690, 693, supra; United States v Garrett, 542 F2d 23, 26; Jackson v State, 695 P2d 227, 230 [Alaska App]), and it must be ascertained whether the defendant is still able to test the truth of the witness’s direct testimony (see, Fountain v United States, 384 F2d 624, 628, cert denied sub nom. Marshall v United States, 390 US 1005; Coil v United States, 343 F2d 573, cert denied 382 US 821), or whether the "answers solicited might have established untruthfulness with respect to the specific events of the crime charged” (United States v Cardillo, 316 F2d 606, 613, cert denied 375 US 822). If bias or interest has been fully explored through other means (United States v Pelusio, 725 F2d 161, 169; United States v Calvente, 722 F2d 1019, 1024-1025, cert denied — US —, 105 S Ct 2030, sub nom. Martinez-Torres v United States, — US —, 106 S Ct 170; United States v Brown, 634 F2d 819, 825-826), or the precluded area involved cumulative matter already presented (see, United States v Phillips, 664 F2d 971, 1027-1028, cert denied sub nom. Platshorn v United States, 459 US 906, sub nom. Myers v United States, 457 US 1136; United States v Diecidue, 603 F2d 535, 552, cert denied sub nom. Antone v United States, 445 US 946), there generally has been no infringement of the right of confrontation.
In the end, as the United States Court of Appeals for the Fifth Circuit put it, "[w]hether the exclusion of particular impeaching evidence creates a substantial danger of prejudice therefore depends, at least in part, on the defendant’s ability to make the same impeachment argument in the absence of excluded evidence” (United States v Brown, 634 F2d 819, 825-826, supra). This, of course, can only be gouged by reference to the facts of a particular case, so it must be "recognize[d] that '[a] trial court has wide discretion to determine whether a witness’s testimony must be stricken because cross-examinatian was restricted’ ” (United States v Seifert, 648 F2d 557, 562, supra, quoting United States v Star, 470 F2d 1214, 1217-1218), and "only in a case of abuse of such discretion resulting in obvious prejudice should an appellate court intervene” (United States v Brierly, 501 F2d 1024, 1027, cert denied 419 US 1052; see, McCormick, Evidence § 140, at 347, n 17 [3d ed]).
m
Defendants point to five areas of cross-examination which they claim were essential to their right of confrontation: (1) the presence of another gang member at the scene, known as *30Timmy Tam, and Hu’s possible involvement in Tam’s murder two weeks later; (2) any promises or threats made by law enforcement authorities to secure Hu’s testimony; (3) Hu’s participation in conversations at the coffee shop; (4) Hu’s leadership of the Ghost Shadows gang; and (5) Hu’s possible involvement in the shooting of defendant Chin six months after the crime. None of these subjects were covered on direct examination, and examination of the challenged subject areas establishes that nothing relevant to Hu’s bias, credibility, or motive, was kept from the jury.3
First, defendants had ample opportunity to advance the theory that Timmy Tam committed the crime, and that Hu later killed Tam in retaliation. Defense counsel asked Hu whether Tam had shot at him on December 23, 1980. Hu was granted immunity and answered "no.” Defense counsel then introduced into evidence a letter signed by the prosecutor stating that Hu was a suspect in the murder of Timmy Tam. Further cross-examination would have been cumulative (United States v Brown, 634 F2d 819, 825-826, supra; United States v Diecidue, 603 F2d 535, 552, supra; United States v Gould, 536 F2d 216, 222; United States v Marcus, 401 F2d 563, 566, cert denied 393 US 1023).
By the same token, Hu’s refusal to answer all of the questions concerning open cases did not effectively deprive defendants of their right of confrontation. The point of these questions was not to establish Hu’s commission of the outstanding offenses, but rather to show that he was charged or suspected of having committed them and thus had a motive to curry favor with a prosecuting authority. In fact, most of the questions related to purported "threats” and "promises” made by law enforcement authorities.
*31The area was sufficiently probed. Hu answered one of the defendants’ questions on the subject, confirming that he had no agreements with the People, other than the immunity that was granted him in court for his testimony. Moreover, the jury was aware that Hu was a suspect in the murder of Timmy Tam and that the People had no understanding with Hu regarding the disposition of that case. The only other open case against Hu was an extortion charge pending in Maryland. Since interest or bias is not collateral, Hu’s statements concerning the crime would not have been binding on the defendants (People v Webster, 139 NY 73; Richardson, Evidence § 491 [10th ed]). Defendants, therefore, could have called witnesses to testify to the existence of the charge. They also could have accepted the People’s stipulation that Hu was involved in that crime, which would have obviated the need to call such witnesses. Defendants did neither.
Thus, unlike Davis v Alaska (415 US 308, supra), in which a prosecutor invoked a State policy to prevent cross-examination of a crucial witness about the fact that he was on probation pursuant to a juvenile adjudication, the People never sought to withhold any relevant impeachment material from the jury. In any event, cross-examination on the issue would have been cumulative, and, in the circumstances of this case, its omission was harmless.
Nor did Hu’s invocation of the privilege against self-incrimination concerning the conversation in the coffee shop deprive defendants of their right to explore material facts. Hu’s participation was fully described by four other witnesses, and even defense counsel conceded at one point that if Hu were to testify on the subject, he would most likely admit that he was having a discussion about "dividing up Mott Street.” Challenging Hu with inconsistencies in the conversations would not have advanced the farfetched claim that no conversation occurred and that the entire incident had been fabricated to cover up police misconduct. Hu’s testimony confirming that the conversation took place would have simply rendered such a theory totally implausible.
Similarly, Hu’s refusal to answer questions about his role as leader of the Ghost Shadows and the gang rivalry did not preclude defendants from establishing Hu’s possible motive to frame defendants. Hu’s violent conduct was placed before the jury by evidence showing that under Hu’s leadership the Ghost Shadows had tried to shoot Nickie Louie and others, *32including defendant Chan. The struggle between Hu and the defendants for control of the extortion rackets in Chinatown was also undeniably established by other evidence. All facts relevant to Hu’s credibility and motive were thus squarely placed before the jury. Merely because some of the evidence was adduced through sources other than cross-examination does not mean that the right of confrontation has been infringed (United States v Pelusio, 725 F2d 161, 169; supra; United States v Calvente, 722 F2d 1019, 1024-1025, supra; United States v Coven, 662 F2d 162, 171; cf. People v Jarvis, 111 AD2d 262).
Finally, defendants now argue, for the first time, that they should have been allowed to question Hu about his supposed involvement in the shooting of defendant Chin in June 1981. Two other men had been arrested for that shooting, and Hu had not been a suspect in that crime. This proposed line of questioning would have added nothing to Hu’s bias and motive to falsify already spread upon the record.
To the extent that defendants would have made Hu their own witness by eliciting new facts and theories, we would note that the prosecutor’s discretion to confer immunity on witnesses called by defendants is quite broad (CPL 50.30; People v Owens, 63 NY2d 824; People v Adams, 53 NY2d 241, 247; People v Shapiro, 50 NY2d 747; People v Sapia, 41 NY2d 160, cert denied 434 US 823). That discretion will not be deemed to have been abused unless, for example, the prosecutor builds his case with immunized witnesses but denies the defendant a similar opportunity (see, e.g., People v Adams, supra, at p 247). Plainly, the defendant’s choice of a victim who is also a criminal does not place the People on the horns of an unacceptable dilemma — either grant the victim absolute immunity for numerous crimes so that the defendants may question him about them or absolutely preclude the victim’s testimony about the defendant’s crime altogether (United States v Pelusio, 725 F2d 161, 169, supra; United States v Brown, 634 F2d 819, 826, supra).
In sum, defendants fully cross-examined Hu on matters covered in direct testimony, and all collateral facts relevant to Hu’s bias, credibility, and motive were established through the cross-examination of Hu and through the testimony of other witnesses. Hu had a valid basis for asserting his privilege against self-incrimination and the People had an equally valid basis for declining to confer immunity upon him since under *33New York law this would have granted Hu full dispensation from criminal liability for any acts discussed in his testimony (CPL 50.20; People v Sobotker, 61 NY2d 44, 47; People v Rappaport, 47 NY2d 308, 313, cert denied 444 US 964).4 In such circumstances, the trial court did not abuse its discretion in declining to strike Hu’s direct testimony (see, People v Stanard, 42 NY2d 74, 85, cert denied 434 US 986; McCormick, Evidence § 140, at 347, n 17 [3d ed]).
IV
Two other issues tendered by defendant Chan warrant but brief discussion.
During a midtrial hearing, a witness testified that Chin had fired a gun at Hu. According to the witness, Chin had said that a person named "Chris” had handed him the gun after "Chris” attempted to fire it, while Peter Chan was pointing at Hu and yelling, "shoot him, shoot him.” Chan argues that this evidence somehow exculpated him and that the People should have disclosed it prior to trial.
We fail to perceive how this evidence is exculpatory. The presence of a person named Chris did not exclude the likelihood that Chan was also one of the gunmen, particularly in a case like this involving a murder plot by gang members. Even if the People had been aware of the evidence prior to that testimony, and they were not, constitutional error occurs only if the evidence which was not disclosed was material in the sense that "there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different” (United States v Bagley, 473 US —, 105 S Ct 3375, 3384), plainly not the case here.
Chan’s remaining contention, that the trial court’s jury instructions were improper because it injected a conspiracy theory into the case, was not preserved for appellate review *34(CPL 470.05 [2]; People v Karabinas, 63 NY2d 871; People v Hoke, 62 NY2d 1022). Chan only objected at trial on the ground the jury should also be instructed that it "must find that the others for whose act * * * a defendant is also liable, must be found to have beyond a reasonable doubt, have committed certain acts”, which was properly denied (see, People v Berkowitz, 50 NY2d 333, 342-343; People v Schwimmer, 47 NY2d 1004, affg 66 AD2d 91). Failure to give the instruction is not asserted as error on this appeal; rather, he presently asserts, that he should not be found guilty merely for agreeing with others or planning the attempted murder.
Accordingly, the orders of the Appellate Division should be affirmed.
Chief Judge Wachtler and Judges Meyer, Simons, Kaye and Alexander concur; Judge Hancock, Jr., taking no part.
In each case: Order affirmed.