I’ll explain the construction of generalized motivic cohomology groups, in the spirit of Voevodsky usual motivic cohomology groups,
but with Chow-Witt groups replacing Chow groups in the machinery. I’ll try to explain why these groups are interesting,
and give some ideas about the proof of a theorem identifying the diagonal part of these generalized motivic cohomology groups
of a field with Milnor-Witt K-theory of that field.
(joint work with Jean Fasel)