Abstract: Howe and Harish-Chandra showed that the germ of the local character of an irreducible admissible complex representation of a p-adic reductive group G lies in a finite-dimensional vector space spanned by Fourier transforms of nilpotent orbital integrals. This expansion encodes some properties of the representation.

Suppose p is very large, and let C be an algebraically closed field with characteristic different from p. For an irreducible admissible C-representation of G we define a "local character expansion" with rational number coefficients. Our definition generalizes the Harish-Chandra--Howe local character expansion and continues to capture part of the properties.