Chtoucas restreints pour les groupes r\'eductifs et param\'etrisation de Langlands locale

We associate to every irreducible representation of a reductive group over a local field of equal characteristics a local Langlands parameter up to semisimplification and prove the compatibility with the global parameterization constructed by the second author. Our method involves stacks of restricted shtukas (which are analogues of truncated Barsotti-Tate groups) and nearby cycles over arbitrary bases.