In January 1997, Marc Rieffel gave a talk at a special session of the Joint Annual Meetings entitled “Multiwavelets and operator algebras”, which related wavelet theory to the K-theory of the (commutative) torus. Rieffel’s talk related the multiresolution analysis theory of wavelets due to S. Mallat and Y.Meyer to a nested sequence of Hilbert modules over continuous functions on the torus, and the theory of projective multi-resolution analyses had its origins here. The talk today will relate some of this theory, as well as discussing some recent developments due to B. Purkis of the University of Colorado, Boulder.