Abstract
We describe a Galois analog of Bernstein's decomposition of the category of smooth representations of p-adic reductive groups, in which the enriched Langlands parameters play the role of irreducible objects. The latter will be divided into series by means of the generalized Springer correspondence. Each such series will then be parameterized by the simple modules of an extended affine Hecke algebra (possibly twisted by 2-cocycle). Finally, we'll show how these results allow us, in many situations, to explicitly construct the local Langlands correspondence.
