Generators and Bernoullian factors for amenable actions and cocycles on their orbits

Using the orbital approach to the entropy theory we extend from Z-actions to general countable amenable group actions T (or provide new short proofs to) the following results: (1) relative and absolute Krieger theorem about finite generating partitions (and its infinite Rokhlin counterpart in case h(T) =∞), (2) relative and absolute Sinai theorem about Bernoullian factors, (3) Thouvenot theorem that every intermediate factor of a relatively Bernoullian action is also relatively Bernoul-lian, (4) Thouvenot theorem that a factor of T with the strong Pinsker property enjoys this property, (5) Smorodinsky-Thouvenot theorem that T can be spanned by three Bernoullian factors, (6) Ornstein-Weiss isomorphism theory for Bernoullian actions of the same entropy (provided that they possess generating partitions with at least 3 elements), (7) there are uncountably many non-equivalent CPE extensions of T of the same relative entropy, etc. In proving these theorems, we were able to bypass the machinery from [OrW] except of the Rokhlin lemma. It is shown that the language of orbit equivalence relations and their cocycles (unlike the standard dynamical one) is well suited for th