Submission: 2004, Aug 20
Recently, V. Chernousov, S. Gille and A. Merkurjev have obtained a decomposition of the motive of an isotropic smooth projective homogeneous variety analogous to the Bruhat decomposition. Using the method of A. Białynicki-Birula and a corollary, which is essentially due to S. del Baño, I generalize this decomposition to the case of a (possibly anisotropic) smooth projective variety homogeneous under the action of an isotropic reductive group. This answers a question of N. Karpenko.
2000 Mathematics Subject Classification:
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