Résumé
Given a Galois covering of complete spin manifolds where the base metric has positive scalar curvature near infinity, we prove that for small enough c > 0, the epsilon spectral projection of the Dirac operator has finite trace in the Atiyah von Neumann algebra. This allows us to define the L-2 index in the even case, and we prove its compatibility with the Xie-Yu higher index and deduce L-2 versions of the classical Gromov-Lawson relative index theorems. Finally, we briefly discuss some Gromov-Lawson L-2 invariants.