In what circumstances will a witness give evidence before a grand jury?

In United States v. Kelly, 540 F.2d 990 (9th Cir.1976), cert. denied, 429 U.S. 1040 (1977), a grand jury was investigating a fraudulent scheme. One of the participants in the scheme appeared before the grand jury and falsely denied any involvement. Id. at 992. This court found that one subject of the grand jury's investigation was the extent of the witness's involvement in the fraud. Id. at 993. We held that the witness's false testimony was material, because "[b]y testifying falsely, he withheld from the grand jury direct evidence of the extent of his personal involvement." Id.