  We introduce a generalization of degenerate affine Hecke algebra, called
wreath Hecke algebra, associated to an arbitrary finite group G. The simple
modules of the wreath Hecke algebra and of its associated cyclotomic algebras
are classified over an algebraically closed field of any characteristic p. The
modular branching rules for these algebras are obtained, and when p does not
divide the order of G, they are further identified with crystal graphs of
integrable modules for quantum affine algebras. The key is to establish an
equivalence between a module category of the (cyclotomic) wreath Hecke algebra
and its suitable counterpart for the degenerate affine Hecke algebra.
