We examine the propagation of two‐dimensional relativistic jets through the stellar progenitor in the collapsar model for gamma‐ray bursts. In agreement with previous studies, we find that the jet is collimated by its passage. Moreover, interaction of the jet with the star causes mixing that sporadically decelerates the jet, leading to a highly variable Lorentz factor. The jet that finally emerges has a moderate Lorentz factor, but a very large internal energy loading. In a second series of calculations we follow the emergence of such enegy‐loaded jets from the star. For the initial conditions chosen, conversion of the remaining internal energy gives a terminal Lorentz factor of approximately 150. Implications of our calculations for GRB light curves, the luminosity‐variability relation, and the GRB‐supernova association are discussed.