We define the Chern character of the index class of a G-invariant family of G-transversally elliptic operators, see [6]. Next we study the Berline-Vergne formula for families in the elliptic and transversally elliptic case.
@article{hal-01873320,
author = {Baldare, Alexandre},
title = {The index of G-transversally elliptic families in cohomology},
journal = {HAL},
volume = {2019},
number = {0},
year = {2019},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01873320}
}
Baldare, Alexandre. The index of G-transversally elliptic families in cohomology. HAL, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/hal-01873320/