  We show how a novel construction of the sheaf of Cherednik algebras on a
quotient orbifold Y=X/G by virtue of formal geometry in author's prior work
leads to results for the sheaf of Cherednik algebra which until recently were
viewed as intractable. First, for every orbit type stratum in $X$, we define a
trace density map for the Hochschild chain complex of the sheaf of Cherednik
algebras, which generalises the standard Engeli-Felder's trace density
construction for the sheaf of differential operators. Second, by means of the
newly obtained trace density maps, we prove an isomorphism in the derived
category of complexes of $\mathbb C_Y[[\hbar]]$-modules which computes the
hypercohomology of the Hochschild chain complex $\mathcal{C}_{\bullet}$ of the
sheaf of formal Cherednik algebras. We show that this hypercohomology is
isomorphic to the Chen-Ruan cohomology of the orbifold $X/G$ with values in the
ring of formal power series $\mathbb C[[\hbar]]$. We infer that the Hochschild
chain complex of the sheaf of skew group algebras $\mathcal{D}_X\rtimes G$ has
a well-defined Euler characteristic which is proportional to the topological
Euler characteristic of $X/G$. Finally, we prove an algebraic index theorem.
