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We show that elliptic classes introduced in  for spaces with infinite fundamental groups yield Novikov's type higher elliptic genera which are invariants of K-equivalence. This include, as a special case, the birational invariance of higher Todd classes studied recently by J.Rosenberg and J.Block-S.Weinberger. We also prove the modular properties of these genera, show that they satisfy a McKay correspondence, and consider their twist by discrete torsion.doi:10.4310/mrl.2008.v15.n3.a10 fatcat:fname72km5fz3o6o4husu7n4k4