A motivic construction of the de Rham-Witt complex

The theory of reciprocity sheaves due to Kahn-Saito-Yamazaki is a powerful framework to study invariants of smooth varieties via invariants of pairs $(X,D)$ of a variety $X$ and a divisor $D$. We develop a generalization of this theory where $D$ can be a $\mathbb{Q}$-divisor. As an application, we provide a motivic construction of the de Rham-Witt complex, which is analogous to the motivic construction of the Milnor $K$-theory due to Suslin-Voevodsky.