It is well known that while inventingthe General Relativity, Albert Einstein was strongly in spired by ideas of Ernst Mach related to the origin of the inertial forces. The extent of agreement between Generalm Relativity and Mach´s ideas is a matter of long discussion. At the present time, there are two widely debated relativistic effects of the Machian origin: dragging of inertial frames and cosmological constant. The present work is devoted to the influence of the repulsive cosmological constant in astrophysical processes related to accretion discs orbiting supermassive black holes in nuclei of giant galaxies.