Quasi-hereditary quotients of finite Chevalley groups and Frobenius kernels, Q

Let G be a semisimple connected simply connected linear algebraic group over an algebraically closed field k of characteristic p> 0. De-note by Gn its n-th Frobenius kernel and by G(pn) its finite subgroup of Fpn-rational points. In this paper we find quotients of the algebra Un = k[Gn] ∗ and of the group algebra kG(pn) whose module cate-gory is equivalent to a (highest weight) subcategory of the category of rational G-modules