  In this note we realize the sheaf of Cherednik algebras $H_{1, c, X, G}$ on a
general good complex orbifold $X/G$, originally introduced by Etingof for
smooth complex varieties with an action by a finite group, by gluing sheaves of
flat sections of flat holomorphic vector bundles on orbit type strata in $X$
which result from a localization procedure. In the case, when $c$ is formal,
this construction can be interpreted as a formal deformation of
$D_X\rtimes\mathbb CG$ via Gel'fand-Kazhdan formal geometry. Contrary to the
original definition of $H_{1, c, X, G}$ the presented construction permits the
computation of trace densities, Hochschild homologies and an algebraic index
theorem for formal deformations of $D_X\rtimes\mathbb CG$. We also hope that
the methods developed here will contribute towards a full proof of
Dolgushev-Etingof's conjecture.
