  The central regions of galaxies are complex environments, rich in evolved
and/or massive stars. For galaxies hosting an active galactic nucleus (AGN)
with jets, the interaction of the jets with the winds of the stars within can
lead to particle acceleration, and to extended high-energy emitting regions. We
compute the non-thermal emission produced by the jet flow shocked by stellar
winds on the jet scale, far from the jet-star direct interaction region. First,
prescriptions for the winds of the relevant stellar populations in different
types of galaxies are obtained. The scenarios adopted include galaxies with
their central regions dominated by old or young stellar populations, and with
jets of different power. Then, we estimate the available energy to accelerate
particles in the jet shock, and compute the transport and energy evolution of
the accelerated electrons, plus their synchrotron and inverse Compton emission,
in the shocked flow along the jet. A significant fraction of the jet energy,
$\sim 0.1-10$\%, can potentially be available for the particles accelerated in
jet-wind shocks in the studied cases. The non-thermal particles can produce
most of the high-energy radiation on jet scales, far from the jet shock region.
This high-energy emission will be strongly enhanced in jets aligned with the
line of sight due to Doppler boosting effects. The interaction of relativistic
jets with stellar winds may contribute significantly to the persistent
high-energy emission in some AGNs with jets. However, in the particular case of
M87, this component seems too low to explain the observed gamma-ray fluxes.
