Given a torsion bundle gerbe on a compact smooth manifold or, more generally, on a compact étale Lie groupoid M, we show that the corresponding category of gerbe modules is equivalent to the category of finitely generated projective modules over an Azumaya algebra on M. This result can be seen as an equivariant Serre-Swan theorem for twisted vector bundles.
Keywords: Gerbe modules, Lie groupoids, Serre-Swann theorem
2010 MSC: 53C08, 55R65, 22A22
Theory and Applications of Categories, Vol. 29, 2014, No. 28, pp 819-835.