  In "Frobenius Categories versus Brauer Blocks", Progress in Math. 274, we
have introduced the Frobenius categories F over a finite p-group P, and we have
associated to F - suitably endowed with some central k*-extensions - a
"Grothendieck group" as an inverse limit of Grothendieck groups of categories
of modules in characteristic p obtained from F, determining its rank. Our
purpose here is to introduce an analogous inverse limit of Grothendieck groups
of categories of modules in characteristic zero obtained from F, determining
its rank and proving that its extension to a field is canonically isomorphic to
the direct sum of the corresponding extensions of the "Grothendieck groups"
above associated with the centralizers in F of a suitable set of
representatives of the F-classes of elements of P.
