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Integrally oriented normally nonsingular maps between singular spaces haveassociated transfer homomorphisms on KO-homology at odd primes. We prove thatsuch transfers preserve Siegel-Sullivan orientations, defined when the singularspaces are compact pseudomanifolds satisfying the Witt condition, for examplepure-dimensional compact complex algebraic varieties. This holds for bundletransfers associated to block bundles with manifold fibers as well as for Gysinrestrictions associated to normally nonsingular inclusions. Our method is basedon constructing a lift of the Siegel-Sullivan orientation to a morphism ofhighly structured ring spectra which factors through L-theory.

Transfer and the Spectrum-Level Siegel-Sullivan KO-Orientation for Singular Spaces