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Polaron cyclotron resonance (CR) has been studied in three modulation-doped GaAs/Al0.3Ga0.7As multiple quantum well structures in magnetic field up to 30 T. Large avoided-level-crossing splittings of the CR near the GaAs reststrahlen region, and smaller splittings in the region of the AlAs-like optical phonons of th AlGaAs barriers, are observed. Based on a comparison with a detailed theoretical calculation, the high frequency splitting, the magnitude of which increases with decreasing well width, is assigned to resonant polaron interactions with AlAs-like interface phonons.