On the group C*-algebras of a semidirect product of commutative and finite groups

Using representations of general position and their properties, we give a description of the group C* -algebras for semidirect products 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 give examples of the group C* -algebras of affine Coxeter groups.