Unipotent almost characters of simple p-adic groups

Understand

Let G be a simple adjoint group and let K=k((\epsilon)) 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 on G(k).
• Using these geometric objects we define the unipotent almost characters of G(K_0) where K_0=F_q((\epsilon)) and state some conjectures relating them to the characters of unipotent representations of G(K_0).