  Let A be a character sheaf on a reductive connected group G over an
algebraically closed field. Assuming that the characteristic is not bad, we
show that for certain conjugacy classes D in G the restriction of A to D is a
local system up to shift; we also give a parametrization of unipotent cuspidal
character sheaves on G in terms of restrictions to conjugacy classes. Without
restriction on characteristic we define canonical bijections from the set of
unipotent character sheaves on G (and from the set of unipotent representations
of the corresponding split reductive group over a finite field) to a set
combinatorially defined in terms of the Weyl group.
