  We study the trace functions in orbiford theory for Z-graded vertex operator
superalgebras and obtain a modular invariance result. More precisely, let V be
a C_2-cofinite Z-graded vertex operator superalgebra and G a finite
automorphism group of V. Then for any commuting pairs (g,h) in G, the
h\sigma-trace functions associated to the simple g-twisted V-modules are
holomorphic in the upper half plane where \sigma is the canonical involution on
V coming from the superspace structure of V. If V is further g-rational for
every g n G, the trace unctions afford a representation for the full modular
group SL(2,Z).
