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Atmospheric-pressure microdischarges excited by nanosecond high-voltage pulses are investigated in helium-nitrogen mixtures by first-principles particle-based simulations, which include VUV resonance radiation transport via the tracing of photon trajectories. The VUV photons, of which the frequency redistribution in the emission processes is included in some detail, are found to modify the computed discharge characteristics remarkably, due to their ability to induce electron emission from the cathode surface. Electrons created this way enhance the plasma density, and a significant increase of the transient current pulse amplitude is observed. The simulations allow the computation of the density of helium atoms in the 21P resonant state, as well as the density of photons in the plasma and the line shape of the resonant VUV radiation reaching the electrodes. These indicate the presence of significant radiation trapping in the plasma and photon escape times longer than the duration of the excitation pulses are found.