Operations in Milnor KK-theory

We show that operations in Milnor KK-theory modpmodp of a field are spanned by divided power operations. After giving an explicit formula for divided power operations and extending them to some new cases, we determine for all fields k0k0 and all prime numbers pp, all the operations KiM/p→KjM/p commuting with field extensions over the base field k0k0. Moreover, the integral case is discussed and we determine the operations KiM/p→KjM/p for smooth schemes over a field.