  We report a detailed study of a model Hamiltonian which exhibits a rich
interplay of geometrical spin frustration, strong electronic correlations, and
charge ordering. The character of the insulating phase depends on the magnitude
of Delta/|t| and on the sign of t. We find a Mott insulator for Delta >> U >>
|t|; a charge transfer insulator for U >> \Delta >> |t|; and a correlated
covalent insulator for U >> \Delta ~ |t|. The charge transfer insulating state
is investigated using a strong coupling expansion. The frustration of the
triangular lattice can lead to antiferromagnetism or ferromagnetism depending
on the sign of the hopping matrix element, t. We identify the "ring" exchange
process around a triangular plaquette which determines the sign of the magnetic
interactions. Exact diagonalization calculations are performed on the model for
a wide range of parameters and compared to the strong coupling expansion. The
regime U >> \Delta ~ |t| and t<0 is relevant to Na05CoO2. The calculated
optical conductivity and the spectral density are discussed in the light of
recent experiments on Na05CoO2.
