Local characters of mod-$\ell$ representations of a $p$-adic reductive group

Abstract

We define the ``lifted character'' of mod-$\ell$ representations of $p$-adic reductive groups where $\ell\not=p$, on compact elements with pro-orders not divisible by $\ell$. We generalize the local character expansion results of Howe, Harish-Chandra and DeBacker to such lifted characters. We show that the result of Moeglin-Waldspurger and Varma on degenerate Whittaker models is valid for the character expansion.