Exercise 14, § 6

Let $G$ be a locally compact group. If $\mathrm{Stell}(G)$ possesses a unit element, then the group $G$ is discrete. (Use the fact that, in the Hilbert space $L^2(G)$, the identity mapping is a norm limit of endomorphisms $\boldsymbol{\gamma }_f$, where $\boldsymbol{\gamma }$ is the left regular representation and where $f\in L^1(G)$.)