A HECKE ACTION ON -MODULES

We construct an action of the affine Hecke category on the principal block $\mathrm {Rep}_0(G_1T)$ of $G_1T$ -modules where G is a connected reductive group over an algebraically closed field of characteristic $p> 0$ , T a maximal torus of G and $G_1$ the Frobenius kernel of G . To define it, we define a new category with a Hecke action which is equivalent to the combinatorial category defined by Andersen-Jantzen-Soergel.