  We extend a recently developed exact schema based, or coarse grained,
formulation of genetic dynamics \cite{stewael,stewael1,stewael2} and its
associated exact Schema theorem to an arbitrary selection scheme and a general
crossover operator. We show that the intuitive``building block'' interpretation
of the former is preserved leading to hierarchical formal solutions of the
equations that upon iteration lead to new results for the limiting distribution
of a population in the case of 1-point crossover and ``weak'' selection, where
we define quantitatively ``weak''. We also derive an exact, analytic form for
the population distribution as a function of time for a flat landscape and
1-point crossover.
