  We investigate various aspects of invariance under local symmetries in the
framework of perturbative algebraic quantum field theory (pAQFT). Our main
result is the proof that the quantum Batalin-Vilkovisky (BV) operator,
on-shell, can be written as the commutator with the interacting BRST charge. Up
to now, this was proven only for a certain class of fields in quantum
electrodynamics and in Yang-Mills theory. Our result is more general and it
holds in a wide class of theories with local symmetries, including general
relativity and the bosonic string. We also comment on other issues related to
local gauge invariance and, using the language of homological algebra, we
compare different approaches to quantization of gauge theories in the pAQFT
framework.
