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 scat tering of cosmic ray (CR) electrons on the cosmic microwave background radi ation and on starlight from our own galaxy. Assuming that the mechanisms ac celerating Galactic CR hadrons and electrons are the same, we derive simple and successful relations between the spectral indices of the GBR above a f ew MeV send the CR electrons and CR nuclei above a few GeV. We reproduce th e observed intensity and angular dependence of the GBR, in directions away from the Galactic disc and centre, without recourse to hypothetical extraga lactic sources.