A condition of geometric modular action is proposed as a selection principl
e for physically interesting states on general space-times. This condition
is naturally associated with transformation groups of partially ordered set
s and provides these groups with projective representations. Under suitable
additional conditions, these groups induce groups of point transformations
on these space-times, which may be interpreted as symmetry groups. The con
sequences of this condition are studied in detail in application to two con
crete spacetimes - four-dimensional Minkowski and three-dimensional de Sitt
er spaces - for which it is shown how this condition characterizes the stat
es invariant under the respective isometry group. An intriguing new algebra
ic characterization of vacuum states is given. In addition, the logical rel
ations between the condition proposed in this paper and the condition of mo
dular covariance, widely used in the literature, are completely illuminated
.