The B(G)-parametrization of the local Langlands correspondence

This article is on the parametrization of the local Langlands correspondence over p-adic fields for non-quasi-split groups according to the philosophy of Vogan. We show that a parametrization indexed by the basic part of the Kottwitz set (which is an extension of the set of pure inner twists) implies a parametrization indexed by the full Kottwitz set. On the Galois side, we consider irreducible algebraic representations of the full centralizer group of the L-parameter (i.e not a component group). These yield sheaves on the stack of Langlands parameters.Comment: 15 page