  The main goal of this paper is to introduce the notion of twisted partial
action of groupoids. We generalize the theorem about the existence of an
enveloping action, also known as the globalization theorem, and show that the
crossed products of the twisted partial action and of its associated twisted
global action are Morita equivalent. Finally, we generalize the concepts of
partial projective representation and partial Schur multiplier for a groupoid,
and we show the interaction between groupoid partial projective representions
and groupoid twisted partial actions.
