  We prove several results concerning the representation of projections on
arbitrary Banach spaces. We also give illustrative examples including an
example of a generalized bi-circular projection which can not be written as the
average of the identity with an isometric reflection. We also characterize
generalized bi-circular projections on $C_0(\Om,X)$, with $\Om$ a locally
compact Hausdorff space (not necessarily connected) and $X$ a Banach space with
trivial centralizer.
