  We employ Hirzebruch-type invariants obtained from iterated p-covers to
investigate concordance of links and string links. We show that the invariants
naturally give various group homomorphisms of the string link concordance group
into L-groups over number fields. We also obtain homomorphisms of successive
quotients of the Cochran-Orr-Teichner filtration. As an application we show
that the kernel of Harvey's $\rho_n$-invariant is large enough to contain a
subgroup with infinite rank abelianization, modulo local knots. As another
application, we show that recently discovered nontrivial 2-torsion examples of
iterated Bing doubles lying at an arbitrary depth of the Cochran-Orr-Teichner
filtration are independent over $\Z_2$ as links, in an appropriate sense. We
also construct similar examples of infinite order links which are independent
over $\Z$.
