Operations on Milnor-Witt K-theory

For all integers n and all homotopy modules M*, we define certain operations KMW n -> M* and show that these generate the M*(k)-module of all (in general nonadditive) operations KMW n -> M* in a suitable sense, if M* is N-graded and has a ring structure. This also allows us to explicitly compute the abelian group Hom(KMWn, KMW m ) and all operations between related theories such as Milnor, Witt and Milnor-Witt K-theory.