Chiral rings and Gliozzi-Scherk-Olive projection in orbifolds

The Gliozzi-Scherk-Olive (GSO) projection in the twisted sector of an orbifold background is sometimes subtle, and incompatible descriptions are found in the literature. Here, from the equivalence of partition functions in Neveu-Schwarz-Ramond and Green-Schwarz formalisms, we give a simple rule of the GSO projection for the chiral rings of string theory in $C^3/Z_n.$ The necessary constructions of chiral rings are given by explicit mode analysis.