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