A remark about a theorem of Skandalis

Abstract

Georges Skandalis exhibited in his work on $K$-nuclearity the first class of $C^{\ast }$-algebras $A$ for which the canonical map $K_{\ast }(A{\otimes }_{max}A)\to K_{\ast }(A{\otimes }_{min}A)$ is not an isomorphism. We show that it is the injectivity that fails (even rationally) in his examples.