  Let V be a representation space of a finite group G. We determine the group
structure of the first homology of the equivariant diffeomorphism group of V.
Then we can apply it to the calculation of the first homology of the
corresponding automorphism groups of smooth orbifolds, compact Hausdorff
foliations, codimension one or two compact foliations and a locally free circle
action on the 3-sphere.
