Almost Representations and Asymptotic Representations of Discrete Groups

We define for discrete finitely presented groups a new property related to their asymptotic representations. Namely we say that a groups has the property AGA if every almost representation generates an asymptotic representation. We give examples of groups with and without this property. For our example of a group $G$ without AGA the group $K^0(BG)$ cannot be covered by asymptotic representations of $G$.Comment: 9 pages, LaTeX 2.0

One more pathology of C*-algebraic tensor products

We define a collection of tensor product norms for C*-algebras and show that a symmetric tensor product functor on the category of separable C*-algebras need not be associative.Comment: 6 page