The characteristic classes of Morita equivalent star products on symplectic manifolds

In this paper we give a complete characterization of Morita equivalent star products on symplectic manifolds in terms of their characteristic classes: two star products star and star' on (M,omega) are Morita equivalent if and only if there exists a symplectomorphism psi : M --> M such that the relative class t(star, psi*(star')) is 2pi i-integral. For star products on cotangent bundles, we show that this integrality condition is related to Dirac's quantization condition for magnetic charges.