Étale differentiable stacks are a generalization of manifolds which include such examples as orbifolds and leaf spaces of foliated manifolds. In this talk we will discuss certain aspects of sheaf theory for étale differentiable stacks and emphasize the role of "the universal étale stack".
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/3639