  Several authors have studied homomorphisms from first homology groups of
modular curves to the second K-group of a cyclotomic ring or a modular curve X.
These maps send Manin symbols in the homology groups to Steinberg symbols of
cyclotomic or Siegel units. We give a new construction of these maps and a
direct proof of their Hecke equivariance, analogous to the construction of
Siegel units using the universal elliptic curve. Our main tool is a 1-cocycle
from GL_2(Z) to the second K-group of the function field of a suitable group
scheme over X, from which the maps of interest arise by specialization.
