  We investigate positron scattering upon endohedrals and compare it with
electron-endohedral scattering. We show that the polarization of the fullerene
shell considerably alters the polarization potential of an atom, stuffed inside
a fullerene. This essentially affects both the positron and electron elastic
scattering phases as well as corresponding cross-sections. Of great importance
is also the interaction between the incoming positron and the target electrons
that leads to formation the virtual positronium. We illustrate the general
trend by concrete examples of positron and electron scattering upon endohedrals
He@C60 and Ar@C60, and compare it to scattering upon fullerene C60. To obtain
the presented results, we have employed new simplified approaches that permit
to incorporate the effect of fullerenes polarizability into the He@C60 and
Ar@C60 polarization potential and to take into account the virtual positronium
formation. Using these approaches, we obtained numeric results that show strong
variations in shape and magnitudes of scattering phases and cross-sections due
to effect of endohedral polarization and virtual positronium formation.
