Spectra of infinite Cayley graphs, examples with pure band spectra

It is shown that there are groups $\mathrm{\Gamma }$ with finite generating sets $S$ such that the adjacency operator of the Cayley graph $\mathrm{C}\mathrm{a}\mathrm{y}(\mathrm{\Gamma },S)$ is a disjoint union of $N$ intervals, for arbitrarily large integers $N$.