2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171678We 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.Comments on lemma 3.1 deleted. Final versionAlgebraic Geometry14J50, 58J03, 14M, 11Ftext