The automorphism groups of finite type $G$-structures on orbifolds

The automorphism group of a $G$-structure of finite type and order $k$ on a smooth $n$-dimensional orbifold is proved to be a Lie group of dimension $n+\dim(\mathfrak{g}+\mathfrak{g}_1+\dots+\mathfrak{g}_{k-1})$, where $\mathfrak{g}_i$ is the $i$-th prolongation of the Lie algebra $\mathfrak{g}$ of a given group $G$. This generalizes the corresponding result by Ehresmann for finite type $G$-structures on manifolds. The presence of orbifold points is shown to sharply decrease the dimension of the automorphism group of proper orbifolds. Estimates are established for the dimension of the isometry group and the dimension of the group of conformal transformations of Riemannian orbifolds, depending on the types of orbifold points.