  In this paper, we study the perturbative aspects of the half-twisted variant
of Witten's topological A-model on a complex orbifold X/G, where G is an
isometry group of X. The objective is to furnish a purely physical
interpretation of the mathematical theory of the Chiral de Rham complex on
orbifolds recently constructed by Frenkel and Szczesny in [Chiral de Rham
complex and orbifolds, arXiv: math.AG/0307181]. In turn, one can obtain a novel
understanding of the holomorphic (twisted) N=2 superconformal structure
underlying the untwisted and twisted sectors of the quantum sigma model, purely
in terms of an obstruction (or a lack thereof) to a global definition of the
relevant physical operators which correspond to G-invariant sections of the
sheaf of Chiral de Rham complex on X. Explicit examples are provided to help
illustrate this connection, and comparisons with their non-orbifold
counterparts are also made in an aim to better understand the action of the
G-orbifolding on the original half-twisted sigma model on X.
