The K-Theory of a Simple Separable Exact C*-Algebra Not Isomorphic to Its Opposite Algebra

Abstract

We construct uncountably many mutually nonisomorphic simple separable stably finite unital exact C$^\ast$-algebras which are not isomorphic to their opposite algebras. In particular, we prove that there are uncountably many possibilities for the $K_0$-group, the $K_1$-group, and the tracial state space of such an algebra. We show that these C*-algebras satisfy the Universal Coefficient Theorem. This is new even for the already known example of an exact C*-algebra nonisomorphic to its opposite algebra produced in earlier work.