We study the formation of the spectra in advection dominated accretion flow
s (ADAFs) around Kerr black holes. We use a Monte Carlo approach and fully
general relativistic treatment to follow the paths of individual photons an
d model their scattering with mildly relativistic, thermal electrons of the
two temperature plasma present in the flow. We study the influence of the
accretion rate, black hole mass, black hole angular momentum, and the stren
gth of the small scale magnetic held present in the plasma on the resulting
spectra. The impact of the black hole angular momentum on the spectra is p
resent and can be distinguished from the influence of changes in other para
meters. This property of the models should be taken into account when model
ing the individual sources and the population of inefficiently accreting bl
ack holes in the Universe.