  The 511 keV electron-positron annihilation line, most recently characterized
by the INTEGRAL/SPI experiment, is highly concentrated towards the Galactic
centre. Its origin remains unknown despite decades of scrutiny. We propose a
novel scenario in which known extragalactic positron sources such as radio jets
of active galactic nuclei (AGN) fill the intergalactic medium with MeV e+e-
pairs, which are then accreted into the Milky Way. We show that interpreting
the diffuse cosmic radio background (CRB) as arising from radio sources with
characteristics similar to the observed cores and radio lobes in powerful AGN
jets suggests that the intergalactic positron-to-electron ratio could be as
high as 10^{-5}, although this can be decreased if the CRB is not all produced
by pairs and if not all positrons escape to the intergalactic medium. Assuming
an accretion rate of one solar mass per year of matter into the Milky Way, a
positron-to-electron ratio of only 10^{-7} is already enough to account for
much of the 511 keV emission of the Galaxy. A simple spherical accretion model
predicts an emission profile highly peaked in the central bulge, consistent
with INTEGRAL observations. However, a realistic model of accretion with
angular momentum would likely imply a more extended emission over the disk,
with uncertainties depending on the magnetic field structure and turbulence in
the galactic halo.
