INFINITE SIMPLE C-ASTERISK-ALGEBRAS AND REDUCED CROSS PRODUCTS OF ABELIAN C-ASTERISK-ALGEBRAS AND FREE GROUPS

Let Gamma = < g(1) > < g(2) > *...* < g(n) > *... be a free product of cyclic groups with generators {g(i)}, and C-r(Gamma, P-Lambda) be the C-algebra generated by the reduced group C*-algebra C-r*Gamma and a set of projections P-Lambda associated with a subset Lambda of {g(i )}. We prove the following: (1) C-r(Gamma, P-Lambda) is *-isomorphic to the reduced cross product C(X-Lambda) x(alpha,r) Gamma for certain Hausdorff compact space X-Lambda constructed from Gamma and its bounda ry partial derivative Gamma. (2) C-r(Gamma, P-Lambda) is either a pur ely infinite, simple C-algebra or an extension of a purely infinite, simple C-algebra, depending on the pair (Gamma, Lambda). (3) C-r*(Gam ma, P-Lambda) is nuclear if and only if the subgroup Gamma(Lambda) gen erated by {g(i)}\Lambda is amenable.