  Blazars in elliptical hosts have a population of red giants surrounding their
jet. These stars can carry large wind-blown bubbles into the jets, leading to
gamma-ray emission through bubble-jet interactions. We study the interaction
dynamics and the gamma-ray emission produced when the bubbles formed by red
giant winds penetrate the jet of a blazar in an elliptical galaxy. First, we
characterized the masses and penetration rates of the red giant wind bubbles
that enter the jet. Then, the dynamical evolution of these bubbles under the
jet impact was analysed analytically and numerically, and the radiation losses
of the particles accelerated in the interaction were characterised. Finally,
the synchrotron and the inverse Compton contributions above 100 MeV were
estimated under different jet magnetic fields, powers, and Lorentz factors. We
find that an analytical dynamical model is a reasonable approximation for the
red giant wind bubble-jet interaction. The radiation produced by these wind
bubbles interacting with a jet can have a duty cycle of up to 1. For realistic
magnetic fields, gamma rays could be detectable from sources within the local
universe, preferentially from those with high Lorentz factors (of about 10),
and this could be a relatively common phenomenon for these sources. For
magnetic fields in equipartition with the jet power, and high acceleration
rates, synchrotron gamma rays may be detectable even for modest Lorentz factors
(of about 3), but with a much lower duty cycle.
