  An action of a locally compact group or quantum group on a factor is said to
be strictly outer when the relative commutant of the factor in the crossed
product is trivial. We show that all locally compact quantum groups can act
strictly outerly on a free Araki-Woods factor and that all locally compact
groups can act strictly outerly on the hyperfinite II_1 factor. We define a
kind of Connes' T invariant for locally compact quantum groups and prove a link
with the possibility of acting strictly outerly on a factor with a given T
invariant. Necessary and sufficient conditions for the existence of strictly
outer actions of compact Kac algebras on the hyperfinite II_1 factor are given.
