Quasi-hereditary quotients of finite Chevalley groups and Frobenius kernels

Let G be a semisimple connected simply connected linear algebraic group over an algebraically closed field k of characteristic p > 0. Denote by Gn its nth 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 category is equivalent to a (highest weight) subcategory of the category of rational G-modules.