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We consider dual frames generated by actions of countable discrete groups ona Hilbert space. Module frames in a class of modules over a group algebra areshown to coincide with a class of ordinary frames in a representation of thegroup. This has applications to shift-invariant spaces and wavelet theory. Oneof the main findings in this paper is that whenever a shift-invariant sub spacein L2(Rn) has compactly supported dual frame generators then it also hascompactly supported bi-orthogonal generators. The crucial part in the proof isa theorem by Swan that states that every finitely generated projective moduleover the Laurent polynomials in n variables is free.

Frames generated by actions of countable discrete groups