  The open string ending on a D-brane with a constant B-field in a pp-wave
Ramond-Ramond background is exactly solvable. The theory is controlled by three
dimensionful parameters: alpha', the mass parameter (RR background times the
lightcone momentum) and the B-field. We quantize the open string theory and
determine the full noncommutative structure. In particular, we find a fully
noncommutative phase space whose noncommutativity depends on all these
parameters. The lightcone Hamiltionian is obtained, and as a consequence of the
nontrivial commutation relations of the theory, new features of the spectrum
are noted. Various scaling limits of the string results are considered.
Physical implications are discussed.
