  The authors have recently shown how direct limits of Hilbert spaces can be
used to construct multi-resolution analyses and wavelets in $L^2(\R)$. Here
they investigate similar constructions in the context of Hilbert modules over
$C^*$-algebras. For modules over $C(\T^n)$, the results shed light on work of
Packer and Rieffel on projective multi-resolution analyses for specific Hilbert
$C(\T^n)$-modules of functions on $\R^n$. There are also new applications to
modules over $C(C)$ when $C$ is the infinite path space of a directed graph.
