  This preprint is based on two articles accepted by MNRAS and ApJ.
  Our aim is to study the evolution of the orbit of a star under the influence
of interactions with an accretion disc in an AGN. The model considered consists
of a low-mass compact object orbiting a supermassive black hole and colliding
periodically with the accretion disc. Gravitational field of the nucleus is
described by the Kerr metric. The star is assumed to move along a geodesic arc
between successive interactions with an equatorial accretion disc. We study the
gravitomagnetic (Lense-Thirring) precession of the trajectory. We do not assume
any particular value for the eccentricity or inclination of the orbit or the
angular momentum of the black hole. We also discuss the periodicity related to
the relativistic shift of the pericenter.
  The model of star-disc interactions has been suggested to explain the X-ray
variability observed in the Seyfert galaxy NGC~6814. We briefly discuss on this
subject.
