  In 1996, Berline and Vergne gave a cohomological formula for the index of a
transversally elliptic operator. In this paper we propose a new point of view
where the cohomological formulae make use of equivariant Chern characters with
generalized coefficients and with compact suppport. This kind of Chern
characters was studied by the authors in a previous paper (see
arXiv:0801.2822).
