  Based on the canonical quantization of open strings ending on D-branes with a
background B field, we construct the open string propagator. We demonstrate the
relation between the T duality of the underlying string theory and the Morita
equivalence of the interpolating general Dirac-Born-Infeld theory on a
noncommutative torus in the nonzero modulus \Phi sector. The general
noncommutative Dirac-Born-Infeld action with the Wess-Zumino terms expressed by
the background R-R fields is shown to be Morita invariant.
