MORITA EQUIVALENCE OF PARTIAL GROUP ACTIONS AND GLOBALIZATION

We consider a large class of partial actions of groups on rings, called regular, which contains all s-unital partial actions as well as all partial actions on C*-algebras. For them the notion of Morita equivalence is introduced, and it is shown that any regular partial action is Morita equivalent to a globalizable one and that the globalization is essentially unique. It is also proved that Morita equivalent s-unital partial actions on rings with orthogonal local units are stably isomorphic. In addition, we show that Morita equivalent s-unital partial actions on commutative rings must be isomorphic, and an analogous result for C*-algebras is also established.