We generalize the Wannier interpolation of the electron-phonon matrix elements to the case of polar-optical coupling in polar semiconductors. We verify our methodological developments against experiments, by calculating the widths of the electronic bands due to electron-phonon scattering in GaAs, the prototype polar semiconductor. The calculated widths are then used to estimate the broadenings of excitons at critical points in GaAs and the electron-phonon relaxation times of hot electrons. Our

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... indings are in good agreement with available experimental data. Finally, we demonstrate that while the Fr\"ohlich interaction is the dominant scattering process for electrons/holes close to the valley minima, in agreement with low-field transport results, at higher energies, the intervalley scattering dominates the relaxation dynamics of hot electrons or holes. The capability of interpolating the polar-optical coupling opens new perspectives in the calculation of optical absorption and transport properties in semiconductors and thermoelectrics.