  We present the first spatially resolved, X-ray spectroscopic study of the 4-8
keV diffuse emission found in the central part of the nearby starburst galaxy
M82 on a few arcsecond scales. The new details that we see allow a number of
important conclusions to be drawn on the nature of the hot gas and its origin
as well as feedback on the ISM. We use archival data from Chandra with an
exposure time of 570 ks. The Fexxv emission at 6.7 keV, expected from
metal-enriched hot gas, is enhanced only in a limited area close to the
starburst disc and is weak or almost absent over the rest of the diffuse
emission, resulting in spatial variations in EW from <0.1 keV to 1.9 keV. This
shows the presence of non-thermal emission due to inverse Compton scattering of
the FIR photons by radio emitting cosmic ray electrons. The morphological
resemblance between the diffuse X-ray, radio, and FIR emission maps supports
this concept. Our decomposition of the diffuse emission spectrum indicates that
~70% of the 4-8 keV luminosity originates from the inverse Compton emission.
The metal-rich hot gas with kT~5 keV makes a minor contribution to the 4-8 keV
continuum, but it accounts for the majority of the observed Fexxv line. This
hot gas appears to emerge from the circumnuclear starburst ring and fill the
galactic chimneys identified as mid-infrared and radio emission voids. The
energetics argument suggests that much of the supernova energy in the starburst
site has gone into creating the chimneys and is transported to the halo. We
argue that a hot, rarefied environment produced by strong supernova feedback
results in displacing the brightest X-ray and radio supernova remnants which
are instead found to reside in GMC. We find a faint X-ray source with a radio
counterpart, close to the kinematic centre of the galaxy and we carefully
examine the possibility that this source is a low-luminosity AGN in ADAF phase.
