  The design of commercially feasible magnetic confinement fusion reactors
strongly relies on the reduced turbulent transport in the plasma edge during
operation in the high confinement mode (H-mode). We present first global
turbulence simulations of the ASDEX Upgrade tokamak edge and scrape-off layer
(SOL) in ITER baseline H-mode conditions. Reasonable agreement with the
experiment is obtained for outboard mid-plane measurements of plasma density,
electron and ion temperature, as well as the radial electric field. The radial
heat transport is underpredicted by roughly a factor 2. These results were
obtained with the GRILLIX code implementing a transcollisional,
electromagnetic, global drift-fluid plasma model, coupled to diffusive
neutrals. The transcollisional extensions include neoclassical corrections for
the ion viscosity, as well as either a Landau-fluid or free-streaming limited
model for the parallel heat conduction. Electromagnetic fluctuations are found
to play a critical role in H-mode conditions. We investigate the structure of
the significant $E \times B$ flow shear, finding both neoclassical components
as well as zonal flows. But unlike in L-mode, geodesic acoustic modes are not
observed. The turbulence mode structure is mostly that of drift-Alfv\'en waves.
However, in the upper part of the pedestal, it is very weak and overshadowed by
neoclassical transport. At the pedestal foot, on the other hand, we find
instead the (electromagnetic) kinetic ballooning mode (KBM), most clearly just
inside the separatrix. Our results pave the way towards predictive simulations
of fusion reactors.
