  Projector equivalences used in the definition of the K-theory of operator
algebras are shown to lead to generalizations of the solution generating
technique for solitons in NC field theories, which has recently been used in
the construction of branes from other branes in B-field backgrounds and in the
construction of fluxon solutions of gauge theories. The generalizations involve
families of static solutions as well as solutions which depend on euclidean
time and interpolate between different configurations. We investigate the
physics of these generalizations in the brane-construction as well as the
fluxon context. These results can be interpreted in the light of recent
discussions on the topology of the configuration space of string fields.
