Towards spetses I

We present a formalization, using data uniquely defined at the level of the Weyl group, of the construction and combinatorial properties of unipotent character sheaves and unipotent characters for reductive algebraic groups o ver an algebraic closure of a finite field. This formalization extends to t he case where the Weyl group is replaced by a complex reflection group, and in many cases we get families of unipotent characters for a mysterious obj ect, a kind of reductive algebraic group with a nonreal Weyl group, the "sp ets".