Simplicity of right-angled Hecke C${}^{\ast }$-algebras

By exploiting properties of boundaries associated with Coxeter groups we obtain a complete characterization of simple right-angled multi-parameter Hecke C${}^{\ast }$-algebras. This extends previous results by Caspers, Larsen and the author. Based on work by Raum and Skalski, we further describe the center and the character space of right-angled Hecke C${}^{\ast }$-algebras.