Hecke algebras and affine flag varieties in characteristic p

Let G be a split semi-simple p-adic group and let H be its Iwahori-Hecke algebra with coefficients in the algebraic closure (F) over bar (p) of F-p Let F be the affine flag variety associated with G. We show, in the simply connected simple case, that the K'-theory of F with coefficients in (F) over bar (p) admits an action of H by Demazure operators and that this provides a model for the regular representation of H. A similar result holds for the affine Grassmannian and the mod p Satake-Hecke algebra of G. (C) 2016 Elsevier B.V. All rights reserved.