Abstract
Let G be a reductive p-adic group, we are interested in finitely generated projective smooth G-modules. Let P be such a module, consider it as a З-module, where З is the Bernstein center of the category of smooth G-modules. Then we can form P ⊗З.χℂ for every complex-valued character of З: it is a finite length smooth representation of G. We describe its image in the Grothendieck group of finite length smooth G-modules. To do this, we define under suitable assumptions a З-valued character on the З-admissible (but not admissible!) representation P. The case of indGK(1) where K is a special compact open subgroup of G is an interesting example. Some of his properties are discussed and extended to other representations of K using Bushnell and Kutzko's theory of types, when G = GL(n).
© Walter de Gruyter
