Semigroup *-Algebras Arising from Graphs of Monoids.

We study groupoids and semigroup |$C^{\ast }$| -algebras arising from graphs of monoids, in the setting of right LCM monoids. First, we establish a general criterion when a graph of monoids gives rise to a submonoid of the fundamental group that is right LCM. Moreover, we carry out a detailed analysis of structural properties of semigroup |$C^{\ast }$| -algebras arising from graphs of monoids, including closed invariant subspaces and topological freeness of the groupoids, as well as ideal structure, nuclearity, and K-theory of the semigroup |$C^{\ast }$| -algebras. As an application, we construct families of pairwise nonconjugate Cartan subalgebras in every UCT Kirchberg algebra. [ABSTRACT FROM AUTHOR]