  The shear viscosity of a gluon gas is calculated using the Green-Kubo
relation. Time correlations of the energy-momentum tensor in thermal
equilibrium are extracted from microscopic simulations using a parton cascade
solving various Boltzmann collision processes. We find that the pQCD based
gluon bremsstrahlung described by Gunion-Bertsch processes significantly lowers
the shear viscosity by a factor of 3-8 compared to elastic scatterings. The
shear viscosity scales with the coupling as 1/(alpha_s^2\log(1/alpha_s)). For a
constant coupling constant the shear viscosity to entropy density ratio has no
dependence on temperature. Replacing the pQCD-based collision angle
distribution of binary scatterings by an isotropic form decreases the shear
viscosity by a factor of 3.
