Chow groups of some generically twisted flag varieties

Abstract

We classify the split simple affine algebraic groups $G$ of types A and C over a field with the property that the Chow group of the quotient variety $E∕P$ is torsion-free, where $P\subset G$ is a special parabolic subgroup (e.g., a Borel subgroup) and $E$ is a generic $G$-torsor (over a field extension of the base field). Examples of $G$ include the adjoint groups of type A. Examples of $E∕P$ include the Severi–Brauer varieties of generic central simple algebras.