The Chow groups of Severi--Brauer varieties associated to biquaternion division algebras were originally computed by Karpenko in the mid nineties. The main difficulty in these computations is determining whether or not CH^2, the group of codimension 2 cycles, contains nontrivial torsion; for these varieties this group is torsion-free. Since his original proof, Karpenko has given two other proofs of this result. All of these proofs involve some clever use of K-theory to determine relations between some explicit cycles. In this talk, I'll discuss a new geometric method that one can use to determine these same relations. Passcode: MSUALG