Lie groupoids are important objects in the study of symmetries, because they encode a broader notion of symmetries than just actions of Lie groups.

It is important, for instance in the context of index theory, to understand the equivariant geometric aspects of a Lie groupoid.

For Lie group-actions this is well-understood in terms of the non-commutative geometry of the convolution algebra and the aim is to generalize these results to Lie groupoids.

In this talk, we will briefly recall Lie groupoids, introduce the relevant parts of non-commutative geometry and discuss results (obtained joint with Hessel Posthuma) relating the deformation theories of a Lie groupoid and that of its convolution algebra.