C∗-algebras associated to directed graphs of groups, and models of Kirchberg algebras

We introduce C & lowast;-algebras associated to directed graphs of groups. In particular, we associate a combinatorial C & lowast;-algebra to each row-finite directed graph of groups with no sources, and show that this C & lowast;-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 & lowast;-algebras (and their Morita equivalent crossed products) contain the class of stable UCT Kirchberg algebras. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).