Traces, Unitary Characters and Crossed Products by Z

Abstract

We determine the character group of the infinite unitary group of a unital exact C∗-algebra in terms of K-theory and traces and obtain a description of the infinite unitary group modulo the closure of its commutator subgroup by the same means. The methods are then used to decide when the state space SK0(A × α Z) of the K0 group of a crossed product by Z is homeomorphic to SK0(A)α or T(A)α. We also consider the crossed productixaGbya discrete countable abelian group G and give necessary and sufficient conditions for the equality T(A ×αG) = T(A)α to hold. © 1995, Research Institute forMathematical Sciences. All rights reserved.