  We argue that the worldvolume theories of D-branes probing orbifolds with
discrete torsion develop, in the large quiver limit, new non-commutative
directions. This provides an explicit `deconstruction' of a wide class of
noncommutative theories. This also provides insight into the physical meaning
of discrete torsion and its relation to the T-dual B field. We demonstrate that
the strict large quiver limit reproduces the matrix theory construction of
higher-dimensional D-branes, and argue that finite `fuzzy moose' theories
provide novel regularizations of non-commutative theories and explicit string
theory realizations of gauge theories on fuzzy tori. We also comment briefly on
the relation to NCOS, (2,0) and little string theories.
