  In 1986, Spencer Bloch gave an abstract definition of a (regulator) map from
higher Chow groups to Deligne-Beilinson cohomology. This map can be defined on
the underlying complexes, and Kerr, Lewis and M\"uller-Stach gave an explicit
description of this map in terms of currents. Using a multiplicative version of
the Deligne complex, we give a commutative version of this map.
