The subdwarf-B pulsator, KIC10553698A, is one of 16 such objects observed with one-minute sampling for most of the duration of the Kepler Mission. Like most of these stars, it displays a rich g-mode pulsation spectrum with several clear multiplets that maintain regular frequency splitting. We identify these pulsation modes as components of rotationally split multiplets in a star rotating with a period of ~41d. From 162 clearly significant periodicities, we are able to identify 156 as likely components of l=1 or l=2 multiplets. For the first time we are able to detect l=1 modes that interpose in the asymptotic period sequences and that provide a clear indication of mode trapping in a stratified envelope, as predicted by theoretical models. A clear signal is also present in the Kepler photometry at 3.387d. Spectroscopic observations reveal a radial-velocity amplitude of 64.8km/s. We find that the radial-velocity variations and the photometric signal have phase and amplitude that are perfectly consistent with a Doppler-beaming effect and conclude that the unseen companion, KIC10553698B, must be a white dwarf most likely with a mass close to 0.6M_{sun}_.