Abstract:

Let $T$ be a split maximal torus of a split semisimple linear algebraic group G over a field k of characteristic 0. Consider the category of G and T-equivariant motives of projective homogeneous G-varieties. We describe an endomorphism ring of the G-motive and T-motive of the total G-flag \amalg_P G/P using the relative push-pull operators.