UNIPOTENT ALMOST CHARACTERS OF SIMPLE p-ADIC GROUPS

Let G be a simple adjoint group and let K = k((is an element of)) where k is an algebraic closure of a finite field F-q. In this paper we define some geometric objects on G(K) which are similar to the (cohomology sheaves of the) unipotent character sheaves of G(k). Using these geometric objects we define the unipotent almost characters of G(K-0) where K-0 = F-q((is an element of)) and state some conjectures relating them to the characters of unipotent representations of G(K-0).