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Recently the operator algebra, including the twisted affine primary fields,and a set of twisted KZ equations were given for the WZW permutation orbifolds.In the first part of this paper we extend this operator algebra to include theso-called orbifold Virasoro algebra of each WZW permutation orbifold. Thesealgebras generalize the orbifold Virasoro algebras (twisted Virasoro operators)found some years ago in the cyclic permutation orbifolds. In the second part,we discuss the reducibility of the twisted affine primary fields of the WZWpermutation orbifolds, obtaining a simpler set of single-cycle twisted KZequations. Finally we combine the orbifold Virasoro algebra and thesingle-cycle twisted KZ equations to investigate the spectrum of each orbifold,identifying the analogues of the principal primary states and fields also seenearlier in cyclic permutation orbifolds. Some remarks about general WZWorbifolds are also included.Comment: 57 pages, typos fixe

EXTENDED OPERATOR ALGEBRA AND REDUCIBILITY IN THE WZW PERMUTATION ORBIFOLDS