Gabor duality theory for Morita equivalent $C^*$-algebras

We establish a duality principle for standard module frames for equivalence bimodules of Morita equivalent $C^*$-algebras, which reduces to the well-known Gabor duality principle for twisted group $C^*$-algebras of a lattice in phase space and the Heisenberg modules as equivalence bimodules. Our approach is based on the localization of a Hilbert $C^*$-module with respect to a trace.
This is joint work with Are Austad and Mads S. Jakobsen.