See file integralcoeff.tex (now moved somewhere else I think, maybe to Open Questions Note)
Goal: Define a regulator from integral coeff motivic cohom or higher Chow groups to integral coeffs Deligne cohomology.
Jakob email Oct 2010: With a huge late-night-fever-disclaimer: I’m currently thinking that we can define a regulator map from BGL into a Deligne cohomology spectrum which takes Betti-cohomology with Z(!!!)-coefficients (and de Rham cohomology of the variety over R or C, as usual). At least in the Riou-style proof of the existence of the regulator, I don’t see why we would need the Betti-cohomology part to be with Q- (or R-) coefficients. If this is true, we actually get sequences which are as Z-coefficient-ish as possible. In particular, for motives over Z, our groups would enjoy a Z-structure (as opposed to a Q-structure only).
See the Cisinski emails in pdf
See Spitzwecks motivic cohomology over Spec Z
nLab page on Integral coefficients regulator