NOTE ON THE MOD p MOTIVIC COHOMOLOGY OF ALGEBRAIC GROUPS

Abstract

Let G_k be a split reductive group over a field k of ch(k) =0 corresponding to a compact Lie group G.Then the mod p motivic cohomology H ^∗,∗´ (G_k;Z/p) is isomorphic to just a tensor product of the usual mod p cohomology of G and the mod p motivic cohomology of the point, when G =SU_n, SO_n,G₂,F₄, or E₆.Moreover, the Kunneth formula holds for cohomology of these groups. However, when G_k is not split over k, the situation is quite different.