  In this paper we will analyze the Fantappie group and its properties in
connection with Cantorian space-time. Our attention will be focused on the
possibility of extending special relativity. The cosmological consequences of
such extension appear relevant, since thanks to the Fantappie group, the model
of the Big Bang and that of stationary state become compatible. In particular,
if we abandon the idea of the existence of only one time gauge, since we do not
see the whole Universe but only a projection, the two models become compatible.
In the end we will see the effects of the projective fractal geometry also on
the galactic and extra-galactic dynamics.
