  The classical Serre-Swan's theorem defines a bijective correspondence between
vector bundles and finitely generated projective modules over the algebra of
continuous functions on some compact Hausdorff topological space. We extend
these results to obtain a correspondence between the category of
representations of an etale Lie groupoid and the category of modules over its
convolution algebra that are of finite type and of constant rank. Both of these
constructions are functorially defined on the Morita bicategory of etale Lie
groupoids and the given correspondence represents a natural equivalence between
them.
