On the Group $C^{*}$-Algebras of a Semidirect Product of Commutative and Finite Groups - Samoilenko, Yu. S.; Yushchenko, K. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 2005)
By using representations of general position and their properties, we give the description of group $C^{*}$-algebras for semidirect products $\mathbb{Z}^d × G_f$, where $G_f$ is a finite group, in terms of algebras of continuous matrix-functions defined on some compact set with boundary conditions. We present examples of the $C^{*}$-algebras of affine Coxeter groups.