  We generalize Rost's theory of cycle modules using Milnor-Witt K-theory
instead of the classical Milnor K-theory. We obtain a (quadratic) setting to
study general cycle complexes and their (co)homology groups. The usual
constructions are developed: proper pushfoward, (essentially) smooth pullback,
long exact sequences, (coniveau) spectral sequences and products, as well as
the homotopy invariance property; in addition, Gysin morphisms for lci maps are
constructed. We prove an adjunction theorem linking our theory to Rost's.
