  We explore the possibility that the diffuse gamma-ray background radiation
(GBR) at high galactic latitudes could be dominated by inverse Compton
scattering of cosmic ray (CR) electrons on the cosmic microwave background
radiation and on starlight from our own galaxy. Assuming that the mechanisms
accelerating galactic CR hadrons and electrons are the same, we derive simple
and successful relations between the spectral indices of the GBR above a few
MeV, and of the CR electrons and CR nuclei above a few GeV. We reproduce the
observed intensity and angular dependence of the GBR, in directions away from
the galactic disk and centre, without recourse to hypothetical extragalactic
sources.
