We give a decomposition of the Chow motive of an isotropic projective homogeneous variety of a semisimple algebraic group in terms of twisted motives of simpler projective homogeneous varieties. As an application, we prove a generalization of Rost's nilpotence theorem.
"Motivic decomposition of isotropic projective homogeneous varieties." Duke Math. J. 126 (1) 137 - 159, 15 January 2005. https://doi.org/10.1215/S0012-7094-04-12614-4