  Non-blazar AGN have been recently established as a class of gamma-ray
sources. M87, a nearby representative of this class, show fast TeV variability
on timescales of a few days. We suggest a scenario of flare gamma-ray emission
in non-blazar AGN based on a red giant interacting with the jet at the base. We
solve the hydrodynamical equations that describe the evolution of the envelope
of a red giant blown by the impact of the jet. If the red giant is at least
slightly tidally disrupted by the supermassive black hole, enough stellar
material will be blown by the jet, expanding quickly until a significant part
of the jet is shocked. This process can render suitable conditions for energy
dissipation and proton acceleration, which could explain the detected day-scale
TeV flares from M87 via proton-proton collisions. Since the produced radiation
would be unbeamed, such an events should be mostly detected from non-blazar
AGN. They may be frequent phenomena, detectable in the GeV-TeV range even up to
distances of $\sim 1$ Gpc for the most powerful jets. The counterparts at lower
energies are expected to be not too bright.} {M87, and nearby non-blazar AGN in
general, can be fast variable sources of gamma-rays through red giant/jet
interactions.
