Brauer Theory for a finite group can be viewed as a method for comparing the
representations of the group in characteristic 0 with those in prime
characteristic. Here we generalize much of the machinery of Brauer theory to
the setting of profinite groups. By regarding Grothendieck groups as functors
we describe corresponding Grothendieck groups for profinite groups, and
generalize the decomposition map, regarded as a natural transformation. We
discuss characters and Brauer characters for profinite groups. We give a
functorial description of the block theory of a profinite group. We finish with
a method for computing the Cartan matrix of a finite group G given the Cartan
matrix for a quotient of G by a normal p-subgroup.Comment: 16 page