  We construct and study a dimensionally reduced effective theory for
high-temperature SU(2) Yang-Mills theory that respects all the symmetries of
the underlying theory. Our main motivation is to study, whether the correct
treatment of the center symmetry can help extend the applicability of the
dimensional reduction procedure towards the confinement transition. After
performing perturbative matching to the full theory at asymptotically high
temperatures, we map the phase diagram of the effective theory using
non-perturbative lattice simulations. We find that at lower temperature the
theory undergoes a second order confining phase transition, in complete analogy
with the full theory, which is a direct consequence of having incorporated the
center symmetry.
