  Following the results known in the case of a finite abelian group action on
$C\sp*$-algebras we prove the following two theorems; 1. an inclusion $P\subset
A$ of (Watatani) index-finite type has the Rokhlin property (is approximately
representable) if and only if the dual inclusion is approximately representable
(has the Rokhlin property). 2. an inclusion $P\subset A$ of (Watatani)
index-finite type has the tracial Rokhlin property (is tracially approximately
representable) if and only if the dual inclusion is tracially approximately
representable (has the tracial Rokhlin property).
  Moreover, we provide an alternate proof of Phillips' theorem about the
relations between tracial Rokhlin action and tracially approximate
representable dual action using a new conceptual framework suggested by
authors.
