Unipotent character sheaves and strata of a reductive group

Let H be a connected reductive group over an algebraically closed field. We define a surjective map from the set CS(H) of unipotent character sheaves on H (up to isomorphism) to the set of strata of H. To do this we use the generalized Springer correspondence. We also give a new parametrization of CS(H) in terms of data coming from bad characteristic. Some minor errors corrected.