We study collective scattering with Bose-Einstein condensates interacting with a high-finesse ring cavity. The condensate scatters the light of a transverse pump beam superradiantly into modes which, in contrast to previous experiments, are not determined by the geometrical shape of the condensate, but specified by a resonant cavity mode. Moreover, since the recoil-shifted frequency of the scattered light depends on the initial momentum of the scattered fraction of the condensate, we show that it is possible to employ the good resolution of the cavity as a filter selecting particular quantized momentum states.PACS numbers: 42.50. Gy, 42.60.Lh, Under certain circumstances optical and matter wave modes can interact on equal footings in a four-wave mixing process [1]. Recent examples for this are the observations of light-induced collective instabilities in cold atomic clouds [2,3]. The instabilities are induced by mutual Bragg scattering of light at a matter wave grating and atoms at an optical standing wave. The scattering takes place as a self-amplified process called matter wave superradiance (MWSR) or collective atomic recoil lasing (CARL) depending on how subsequent scattering events are correlated. In the case of MWSR, the correlations are stored in long-lived matter wave interferences developing in an ultracold cloud [2]. In general, the scattered photons rapidly leave the interaction volume, thus limiting the coherence time of the optical mode. In the case of CARL, the decay is controlled by recycling the scattered photons in a high-finesse ring cavity. As a consequence, the correlations between scattering events can also be stored in long-lived optical modes of the cavity [4,5].The interaction of ultracold atoms with optical cavities has been studied in several experiments [6][7][8] aiming at reaching the strong coupling limit, where cavity quantum electrodynamics (CQED) can be studied with Bose-Einstein condensed (BEC) atomic clouds. Coupling strengths exceeding not only the cavity decay rate, but also the natural decay rate of the excited atomic state are achieved with microcavities. The mode volumes of these cavities are small enough for a single photon to produce a field strength saturating the atomic transition. However, a small mode volume necessarily implies a poor spectral resolution of the cavity.In this Letter, using a large ring cavity (round trip length L = 87 mm) with a very high finesse of F = 135000, we address the opposite regime characterized by an extremely high resolution on the order of the recoil frequency. At the same time, we maintain the collective coupling strong. A BEC located inside the cavity is illuminated from the side with a pump laser pulse. Using collective scattering in a combination of MWSR and CARL as a probe, we demonstrate the cavity's dramatic impact on the light scattering in two ways. First, we show that the cavity is able to lift the superradiant gain above threshold provided it is resonant with the scattered light. The cavity frames the direction of the superradi...