  We give a unifying description of all inequivalent vector bundles over the
2-dimensional sphere $S^2$ by constructing suitable global projectors $p$ via
equivariant maps. Each projector determines the projective module of finite
type of sections of the corresponding complex rank 1 vector bundle over $S^2$.
The canonical connection $\nabla = p \circ d$ is used to compute the
topological charges. Transposed projectors gives opposite values for the
charges, thus showing that transposition of projectors, although an isomorphism
in K-theory, is not the identity map. Also, we construct the partial isometry
yielding the equivalence between the tangent projector (which is trivial in
K-theory) and the real form of the charge 2 projector.
