  We construct a class of exact ground states for correlated electrons on
pentagon chains in the high density region and discuss their physical
properties. In this procedure the Hamiltonian is first cast in a positive
semidefinite form using composite operators as a linear combination of creation
operators acting on the sites of finite blocks. In the same step, the
interaction is also transformed to obtain terms which require for their minimum
eigenvalue zero at least one electron on each site. The transformed Hamiltonian
matches the original Hamiltonian through a nonlinear system of equations whose
solutions place the deduced ground states in restricted regions of the
parameter space. In the second step, nonlocal product wave functions in
position space are constructed. They are proven to be unique ground states
which describe non-saturated ferromagnetic and correlated half metallic states.
These solutions emerge when the strength of the Hubbard interaction $U_i$ is
site dependent inside the unit cell. In the deduced phases, the interactions
tune the bare dispersive band structure such to develop an effective upper flat
band. We show that this band flattening effect emerges for a broader class of
chains and is not restricted to pentagon chains. For the characterization of
the deduced solutions, uniqueness proofs, exact ground state expectation values
for long-range hopping amplitudes and correlation functions are also
calculated. The study of physical reasons which lead to the appearance of
ferromagnetism has revealed a new mechanism for the emergence of an ordered
phase, described here in details (because of lack of space see the continuation
in the paper).
