  We show that the additive higher Chow groups of regular schemes over a field
induce a Zariski sheaf of pro-differential graded algebras, whose Milnor range
is isomorphic to the Zariski sheaf of big de Rham-Witt complexes. This provides
an explicit cycle-theoretic description of the big de Rham-Witt sheaves.
Several applications are derived.
