Abstract
Let G be a split semi-simple p-adic group and let H be its Iwahori-Hecke algebra with coefficients in the algebraic closure k of the finite field with p elements. Let F be the affine flag variety over k associated with G. We show, in the simply connected simple case, that a torus-equivariant K'-theory of F (with coefficients in k) admits an H-action by Demazure operators and that this provides a model for the regular representation of H.
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