  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
Bialynicki-Birula, 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.
