NOTE ON THE MOD p MOTIVIC COHOMOLOGY OF ALGEBRAIC GROUPS

Let Gk 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 ∗,∗´ (Gk;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 =SUn, SOn,G2,F4, or E6.Moreover, the Kunneth formula holds for cohomology of these groups. However, when Gk is not split over k, the situation is quite different.