Abstract
Let $F$ be a non-archimedean local field and let $G$ be a connected reductive group defined over $F$. We assume that $G$ splits over a tame extension of $F$ and that the residual characteristic $p$ does not divide the order of the Weyl group. To each discrete Langlands parameter of the Weil group of $F$ into the complex $L$-group of $G$ we associate explicitly a finite set of irreducible supercuspidal representations of $G(F)$, and relate its internal structure to the centralizer of the parameter. We give evidence that this assignment is an explicit realization of the local Langlands correspondence
