We show that indecomposable weak Kac algebras are free over their Cartan
subalgebras and prove a duality theorem for their actions. Using this result,
for any biconnected weak Kac algebra we construct a minimal action on the
hyperfinite II_1 factor. The corresponding crossed product inclusion of II_1
factors has depth 2 and an integer index. Its first relative commutant is, in
general, non-trivial, so we derive some arithmetic properties of weak Kac
algebras from considering reduced subfactors.