**M-F. Vigneras**

University of Paris, Jussieu

January 2, 2014

**The pro-p-Iwahori Hecke algebra**:
The pro-p-Iwahori Hecke algebra H of a reductive p-adic group G over a
commutative ring R is a deformation of the R-algebra of a variant of an affine Weyl group. When R is a field of characteristic p, it is an important tool to study the R-representations of G, and deep relations between the H-modules and the representations of local Galois groups have been discovered. We will describe the Ram-Goertze alcove walks bases of H and the Bernstein relations, essential to understand the structure of H and its modules.