Abstract

We introduce C⁎-algebras associated to directed graphs of groups. In particular, we associate a combinatorial C⁎-algebra to each row-finite directed graph of groups with no sources, and show that this C⁎-algebra is Morita equivalent to the crossed product coming from the corresponding group action on the boundary of a directed tree. Finally, we show that these C⁎-algebras (and their Morita equivalent crossed products) contain the class of stable UCT Kirchberg algebras.

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