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, Preprint, 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.