  The structure of the Connes-Kreimer renormalization Hopf algebra is studied
for gauge theories, with particular emphasis on the BRST-formalism. We work in
the explicit example of quantum chromodynamics, the physical theory of quarks
and gluons. A coaction of the renormalization Hopf algebra is defined on the
coupling constants and the fields. In this context, BRST-invariance of the
action implies the existence of certain Hopf ideals in the renormalization Hopf
algebra, encoding the Slavnov-Taylor identities for the coupling constants.
