On the algebraic K-theory of some homogeneous varieties, by Alexey Ananyevskiy

In this paper the K-theory of the inner twisted forms of the homogeneous varieties G/H with the connected reductive algebraic groups H < G of the same rank is computed. We provide an explicit isomorphism with the K-theory of certain central simple algebras associated to the considered variety, as a consequence one has that K_0(G/H) is a free abelian group of rank [W(G):W(H)]. The result is used for computing the K-theory of some affine homogeneous varieties including the octonionic projective plane and the quaternionic projective spaces.

Alexey Ananyevskiy <alseang@gmail.com>