# Journal of Operator Theory

Volume 45, Issue 2, Spring 2001 pp. 251-264.

K-theory of simple $C^*$-algebras associated with free products of cyclic groups**Authors**: Wojciech Szymanski (1), and Shuang Zhang (2)

**Author institution:**(1) Department of Mathematics, The University of Newcastle, Newcastle, NSW 2308, Australia

(2) Department of Mathematical S ciences, University of Cincinnati, Cincinnati, Ohio 45221-0025, USA

**Summary:**Let $\Gamma_\Lambda\leq\Gamma$ be free products of countably many cyclic groups and let $C(X_\Lambda)\times\Gamma$ denote the crossed product related to an action of $\Gamma$ on a compact space $X_\Lambda$ constructed from the homogeneous space $\Gamma/\Gamma_\Lambda$ and the boundary $\partial \Gamma$. Assuming that either $\Gamma$ is free or $\Gamma_\Lambda$ is finite we determine the {\rm K}-groups of the crossed products. Among the algebras considered there are both extensions of some Cuntz-Krieger algebras by the compacts and some purely infinite simple $C^*$-algebras (nuclear or not).

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