  We define an Artin stack which may be considered as a substitute for the
non-existing (or empty) moduli space of stable two-pointed curves of genus
zero. We show that this Artin stack can be viewed as the first term of a cyclic
operad in the category of stacks. Applying the homology functor we obtain a
linear cyclic operad. We formulate conjectures which assert that cohomology of
a smooth projective variety has the structure of an algebra over this homology
operad and that gravitational quantum cohomology can naturally expressed in
terms of this algebra. As a test for these conjectures we show how certain
well-known relations between gravitational correlators can be deduced from
them.
