Motivic decompositions of projective homogeneous varieties and change of coefficients

Abstract

We prove that under some assumptions on an algebraic group G, indecomposable direct summands of the motive of a projective G-homogeneous variety with coefficients in F p remain indecomposable if the ring of coefficients is any field of characteristic p. In particular for any projective G-homogeneous variety X, the decomposition of the motive of X in a direct sum of indecomposable motives with coefficients in any finite field of characteristic p corresponds to the decomposition of the motive of X with coefficients in F p . We also construct a counterexample to this result in the case where G is arbitrary.