  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).
