Purely infinite, simple C∗-algebras arising from free product constructions

Abstract. In the reduced free product of C{algebras, (A; ) = (A1; 1) (A2; 2) with respect to faithful states 1 and 2, A is purely innite and simple if A1 is a reduced crossed product B o;r G for G an innite group, if 1 is well behaved with respect to this crossed product decomposition, if A2 6 = C and if is not a trace. The reduced free product construction for C{algebras was invented indepen-dently by Voiculescu [11] and, in a more limited sense, Avitzour [1]. (The term \reduced " is to distinguish this construction from the universal or \full " free prod-uct of C{algebras.) It is a natural construction in Voiculescu's free probability theory (see [12]). Given unital C{algebras A with states whose GNS represen-tations are faithful ( 2 I), the construction yields (A; )