Dark matter clustered in galaxies or clusters is usually interpreted as a new type of material substance subject only to gravitational force. Alternative explanations envisage deviations of the laws of gravity, of the equations of motion or of both from their commonly accepted form. The additional possibility is explored here that the true origin of the effects depicted as "dark matter" should be seen in connection with local violations of the inertia principle, resulting from the quantized granular structure of the cosmic inertial field. Within the framework of Fantappié-Arcidiacono Projective General Relativity (PGR), this quantization appears to be the dual of that of elementary particle masses, which has been suggested for a long time. This hypothesis does not appear to contradict known facts relating to galaxy rotation and to gravitational lensing of clusters. Furthermore, it introduces a new timescale for the coupling of space expansion with structure formation, which could be of interest in cosmology.