  In this paper, we describe non-abelian gauge bundles with magnetic and
electric fluxes on higher dimensional noncommutative tori. We give an explicit
construction of a large class of bundles with nonzero magnetic 't Hooft fluxes.
We discuss Morita equivalence between these bundles. The action of the duality
is worked out in detail for the four-torus. As an application, we discuss
Born-Infeld on this torus, as a description of compactified string theory. We
show that the resulting theory, including the fluctuations, is manifestly
invariant under the T-duality group SO(4,4;Z). The U-duality invariant BPS
mass-formula is discussed shortly. We comment on a discrepancy of this result
with that of a recent calculation.
