On the linearization theorem for proper Lie groupoids

ÐWe revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the Þxed point case (known as ZungÕs theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passage to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance.We also clarify the precise statements of the Linearization Theorem (there has been some confusion on this, which has propagated throughout the existing literature).