Group actions on quantum bundles

Suppose we are given a group G acting through canonical transformations on a symplectic manifold (M, ω). If there is a quantum bundle over (M, ω), a carrier for wave functions in the geometric quantization theory, then G acts infinitesimally on the bundle in a natural way. We give a necessary and sufficient condition for the infinitesimal G-action to integrate up to a global G-action. This is used for an investigation how the choice of the quantum bundle over (M, ω) influences the integrability of the corresponding infinitesimal G-action. The relationship to group representations is briefly mentioned.