# Publications of the Research Institute for Mathematical Sciences

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**Volume 31, Issue 6, 1995, pp. 1011–1029**

**DOI: 10.2977/prims/1195163594**

Traces, Unitary Characters and Crossed Products by ℤ

Klaus Thomsen^{[1]}(1) Matematisk Institute, Aarhus University, Ny Munkegade, 8000, AARHUS C, DENMARK

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 *SK*_{0}(*A* x ℤ) of the *K*_{0} group of a crossed product by ℤ is homeomorphic to *SK*_{0}(*A*)_{α*} or *T*(*A*)_{α*}. We also consider the crossed product *A* x _{α}*G* by a discrete countable abelian group *G* and give necessary and sufficient conditions for the equality *T*(*A* x _{α}*G*) = *T*(*A*)_{α} to hold.

*Keywords: *

Thomsen Klaus: Traces, Unitary Characters and Crossed Products by ℤ. *Publ. Res. Inst. Math. Sci.* 31 (1995), 1011-1029. doi: 10.2977/prims/1195163594