The representation ring of a compact Lie group revisited

We describe a new construction of the induction homomorphism for representation rings of compact Lie groups: a homomorphism first defined by Graeme Segal. The idea is to first define the induction homomorphism for class functions, and then show that this map sends characters to characters. This requires a detection theorem - a class function of G is a character if its restrictions to certain subgroups of G are characters - which in turn requires a review of the representation theory for nonconnected compact Lie groups.