  Using the theory of weakly proper actions of locally compact groups recently
developed by the authors, we give a unified proof of both reduced and maximal
versions of Mansfield's Imprimitivity Theorem and obtain a general version of
Landstad's Duality Theorem for twisted group coactions. As one application, we
obtain the stabilization trick for arbitrary twisted coactions, showing that
every twisted coaction is Morita equivalent to an inflated coaction.
