Exotic group C*-algebras

Let $\mathrm{\Gamma }$ be a discrete group. When $\mathrm{\Gamma }$ is nonamenable, the reduced and full group $C$-algebras differ and it is generally believed that there should be many intermediate $C$-algebras, however few examples are known. In this paper we give new constructions and compare existing constructions of intermediate group $C$*-algebras for both generic and specific groups $\mathrm{\Gamma }$.