  We consider transfer maps on ordinary homology, bordism of singular spaces
and homology with coefficients in Ranicki's symmetric L-spectrum, associated to
block bundles with closed oriented PL manifold fiber and compact polyhedral
base. We prove that if the base polyhedron is a Witt space, for example a
pure-dimensional compact complex algebraic variety, then the symmetric
L-homology orientation of the base, constructed by Laures, McClure and the
author, transfers to the L-homology orientation of the total space. We deduce
from this that the Cheeger-Goresky-MacPherson L-class of the base transfers to
the product of the L-class of the total space with the cohomological L-class of
the stable vertical normal microbundle.
