Heisenberg-Weyl Representations and Morita equivalence for crossed products of Noncommutative solenoids

We study strong Morita equivalence for crossed products of noncommutative solenoids by cyclic groups. Using their description as twisted group $\mathrm C^*$-algebras, we construct automorphisms induced by the natural linear action of $\mathrm{SL}_2(\mathbb Z[1/p])$ on $\mathbb Z[1/p]^2$, for every i