Asymptotic representations of the reduced C*-algebra of a free group: an example

Abstract

We give an example of a non-trivial asymptotic representation of the reduced C*-algebra of a free group. This example allows to evaluate the asymptotic tensor C*-norm of some elements in tensor product C*-algebras and to show semi-invertibility of the non-invertible extension of $C^*_r(\mathbb F_2)$ considered by Haagerup and Thorbjornsen.