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The gamma-rays from gamma-ray bursts (GRBs) are believed to be produced byinternal shocks driven by small timescale, ~1 ms, variation in the GRBoutflows, and a pair-production spectral cutoff is generally expected aroundthe GeV range. However, the observed optical flashes accompanying GRBs suggestthat the delayed residual collisions due to large timescale variation continueto accelerate electrons. We show here that the inverse-Compton (IC) scatteringof the prompt gamma-rays by these residual internal shock electrons leads to ahigh energy emission beyond the previously thought spectral cutoff, inagreement with the previous detections of GeV photons by EGRET in several GRBsin conjunction with MeV emission. We expect a spectral break due to thetransition from the primary to residual internal shock emission at thepreviously thought spectral cutoff, and expect systematic time delays of highenergy photons relative to MeV emission, the discovery of which would providestringent constraint on the outflow properties, but requires large enoughcollection of high energy photons by, e.g., Fermi and AGILE satellites.  The recent Fermi-detected bright GRB 080916c unambiguously shows the shiftingof the prompt emission toward later times as the photon energy increases, aspredicted in the residual collision model. The detected prompt, highest energyphoton (about 70 GeV in the rest frame of the GRB) may not be produced byprimary internal shocks but by IC emission in residual collisions. With themethod involving time delays of high energy emission, the bulk Lorentz factorof GRB 080916c is determined to be \Gamma ~ 300.

Prompt GeV Emission from Residual Collisions in GRB Outflows: Evidence from Fermi Observations of GRB 080916c