The most common progenitors of gamma-ray bursts (GRBs) are massive stars with strong stellar winds. We show that the GRB blast wave in the wind should emit a bright GeV flash. It is produced by inverse-Compton cooling of the thermal plasma behind the forward shock. The main part of the flash is shaped by scattering of the prompt MeV radiation (emitted at smaller radii) which streams through the external blast wave. The inverse-Compton flash is bright due to the huge e ± enrichment of the external medium by the prompt radiation ahead of the blast wave. At late times, the blast wave switches to normal synchrotron-self-Compton cooling. The mechanism is demonstrated by a detailed transfer simulation. The observed prompt MeV radiation is taken as an input of the simulation; we use GRB 080916C as an example. The result reproduces the GeV flash observed by the Fermi telescope. It explains the delayed onset, the steep rise, the peak flux, the time of the peak, the long smooth decline, and the spectral slope of GeV emission. The wind density required to reproduce all these features is typical of Wolf-Rayet stars. Our simulation predicts strong TeV emission 1 minute after the burst trigger; then a cutoff in the observed high-energy spectrum is expected from absorption by extragalactic background light. In addition, a bright optical counterpart of the GeV flash is predicted for plausible values of the magnetic field; such a double (optical+GeV) flash has been observed in GRB 130427A.
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