  We show that elliptic classes introduced in our earlier paper 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.
