  We introduce a notion of rank completion for bi-modules over a finite tracial
von Neumann algebra. We show that the functor of rank completion is exact and
that the category of complete modules is abelian with enough projective
objects. This leads to interesting computations in the L^2-homology for tracial
algebras. As an application, we also give a new proof of a Theorem of Gaboriau
on invariance of L^2-Betti numbers under orbit equivalence.
