Groupoids and the integration of lie algebroids

We show that a Lie algebroid on a stratified manifold is integrable if, and only if, its restriction to each strata is integrable. These results allow us to construct a large class of algebras of pseudodifferential operators. They are also relevant for the definition of the graph of certain singular foliations of manifolds with corners and the construction of natural algebras of pseudodifferential operators on a given complex algebraic variety.