  We generalize the definition of orbifold elliptic genus, and introduce
orbifold genera of chromatic level h, using h-tuples rather than pairs of
commuting elements. We show that our genera are in fact orbifold invariants,
and we prove integrality results for them. If the genus arises from an
H-infinity-map into the Morava-Lubin-Tate theory E_h, then we give a formula
expressing the orbifold genus of the symmetric powers of a stably almost
complex manifold M in terms of the genus of M itself. Our formula is the
p-typical analogue of the Dijkgraaf-Moore-Verlinde-Verlinde formula for the
orbifold elliptic genus. It depends only on h and not on the genus.
