  Following the operator algebraic approach to Gabor analysis, we construct
frames of translates for the Hilbert space localisation of the Morita
equivalence bimodule arising from a groupoid equivalence between Hausdorff
groupoids, where one of the groupoids is \'{e}tale and with a compact unit
space. For finitely generated and projective submodules, we show these frames
are orthonormal bases if and only if the module is free. We then apply this
result to the study of localised Wannier bases of spectral subspaces of
Schr\"{o}dinger operators with atomic potentials supported on (aperiodic)
Delone sets. The noncommutative Chern numbers provide a topological obstruction
to fast-decaying Wannier bases and we show this result is stable under
deformations of the underlying Delone set.
