  We report deep optical integral-field spectroscopy with the MUSE of the
luminous radio-quiet QSO PG1307+085 (z=0.154) obtained during the commissioning
of the instrument. Given the high sensitivity and spatial resolution delivered
by MUSE, we are able to resolve the compact ($r_e$~1.3") elliptical host
galaxy. After careful spectroscopic deblending of the QSO and host galaxy
emission, we infer a stellar velocity dispersion of $155\pm19$km/s. This places
PG1307+085 local $M_{BH}-\sigma_*$ relation within the intrinsic scatter but
offset towards a higher black hole mass with respect to the mean relation. The
observations with MUSE also reveal a large extended ENLR around PG1307+085
reaching out to 30kpc. In addition, we detect a faint bridge of ionized gas
towards the most massive galaxy of the galaxy group being just 20" (50kpc)
away. Previous long-slit spectroscopic observations missed most of these
extended features due to a miss-aligned slit. The ionized gas kinematics does
not show any evidence for gas outflows on kpc scales despite the high QSO
luminosity of $L_\mathrm{bol}>10^{46}$ erg/s. Based on the ionized gas
distribution, kinematics and metallicity we discuss the origin of the ENLR with
respect to its group environments including minor mergers, ram-pressure
stripping or filamentary gas accretion as the most likely scenarios. We
conclude that PG1307+085 is a normal elliptical host in terms of the scaling
relations, but that the gas is most likely affected by the environment through
gravity or ambient pressure. It is possible that the ongoing interaction with
the environment, mainly seen in the ionized gas, is also be responsible for
driving sufficient gas to feed the black hole at the centre of the galaxy.
