Is the diffuse $\gamma$ background radiation generated by galactic cosmic rays?

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.