A general Simonenko local principle and Fredholm condition for isotypical components

In this paper, we derive, from a general Simonenkos local principle, Fredholm criteria for restriction to isotypical components. More precisely, we gave a full proof, of the equivariant local principle for restriction to isotypical components of invariant pseudodifferential operators announced in cite{BCLN2}. Furthermore, we extend this result by relaxing the hypothesis made in the preceding quoted paper.