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Context. OB stars are important building blocks of the Universe, but we have only a limited sample of them well understood enough from an asteroseismological point of view to provide feedback on the current evolutionary models. Our study adds one special case to this sample, with more observational constraints than for most of these stars. Aims. Our goal is to analyse and interpret the pulsational behaviour of the B3 IV star HD 43317 using the CoRoT light curve along with the ground-based spectroscopy gathered by the Harps instrument. This way we continue our efforts to map the Beta Cep and SPB instability strips. Methods. We used different techniques to reveal the abundances and fundamental stellar parameters from the newly-obtained high-resolution spectra. We used various time-series analysis tools to explore the nature of variations present in the light curve. We calculated the moments and used the pixel-by-pixel method to look for line profile variations in the high-resolution spectra. Results. We find that HD 43317 is a single fast rotator (v_rot ~ 50% v_crit) and hybrid SPB/Beta Cep-type pulsator with Solar metal abundances. We interpret the variations in photometry and spectroscopy as a result of rotational modulation connected to surface inhomogeneities, combined with the presence of both g and p mode pulsations. We detect a series of ten consecutive frequencies with an almost constant period spacing of 6339 s as well as a second shorter sequence consisting of seven frequencies with a spacing of 6380 s. The dominant frequencies fall in the regime of gravito-inertial modes., Accepted for publication in Astronomy and Astrophysics on 21/03/2012, 13 pages, 10 figures, 6 tables