  We study global-local mixing for a family of accessible skew products with an
exponentially mixing base and non-compact fibers, preserving an infinite
measure. For a dense set of almost periodic global observables, we prove rapid
mixing; and for a dense set of global observables vanishing at infinity, we
prove polynomial mixing. More generally, we relate the speed of mixing to the
"low frequency behaviour" of the spectral measure associated to our global
observables. Our strategy relies on a careful choice of the spaces of
observables and on the study of a family of twisted transfer operators.
