  We associate a cohomological invariant to each outer action of a group on a
factor, and classify them by the invariant in the case that the group is a
countable discrete amenable group and the factor is appoximately finite
dimensional. The invariant defined for the group Out(M)=Aut(M)/Int(M) is called
the intrinsic modular obstruction. The invariant for an outer action alpha is
given as the pull back of the intrinsic modular obstruction, which is called
the modular obstruction of alpha and denoted by Ob_m(alpha). This is the first
part of the theory and presents general theory. In the case that the factor is
not of type III_0, the invariant is substantially simplified. These cases and
examples will be discussed in forthcoming paper.
