In this paper we analyze the obstructions to the existence of global
action-angle variables for regular non-commutative integrable systems (NCI
systems) on Poisson manifolds. In contrast with local action-angle variables,
which exist as soon as the fibers of the momentum map of such an integrable
system are compact, global action-angle variables rarely exist. This fact was
first observed and analyzed by Duistermaat in the case of Liouville integrable
systems on symplectic manifolds and later by Dazord-Delzant in the case of
non-commutative integrable systems on symplectic manifolds. In our more general
case where phase space is an arbitrary Poisson manifold, there are more
obstructions, as we will show both abstractly and on concrete examples. Our
approach makes use of a few new features which we introduce: the action bundle
and the action lattice bundle of the NCI system (these bundles are canonically
defined) and three foliations (the action, angle and transverse foliation),
whose existence is also subject to obstructions, often of a cohomological
nature