The electronic stopping of a fast, charged particle in a lattice-periodic structure is treated by linear response theory. The energy loss in open crystal channels is found to be reduced due to destructive interference of umklapp scattering processes with small momentum transfer. A sum rule for the first reciprocal moment of the velocity-dependent stopping power is derived, which can be expressed in terms of the static inverse dielectric function. Quantitative information about the importance of the crystal potential is obtained by first-principles pseudopotential calculations. The averaged stopping power in the 110 channel in Si is calculated to be smaller by 30% compared to nonchanneling directions. The sum-rule calculations in the local-density approximation agree with the band-structure results within 20% and are used to discuss the electronic stopping in other semiconductors.