We prove that the motivic cohomology of mixed characteristic schemes, introduced in our previous work, satisfies various expected properties of motivic cohomology, including a motivic refinement of Weibel's vanishing in algebraic K-theory, the projective bundle formula, a comparison to Milnor K-theory, and a universal characterisation in terms of pro cdh descent. These results extend those of Elmanto--Morrow to schemes which are not necessarily defined over a field.
Tess Bouis (Tue,) studied this question.