  Using ideas of S. Wassermann on non-exact $C^*$-algebras and property T
groups, we show that one of his examples of non-invertible C*-extensions is not
semi-invertible. To prove this, we show that a certain element vanishes in the
asymptotic tensor product. We also show that a modification of the example
gives a C*-extension which is not even invertible up to homotopy.
