  We describe an algebraic approach to the time-dependent noncommutative
geometry of a six-dimensional Cahen-Wallach pp-wave string background supported
by a constant Neveu-Schwarz flux, and develop a general formalism to construct
and analyse quantum field theories defined thereon. Various star-products are
derived in closed explicit form and the Hopf algebra of twisted isometries of
the plane wave is constructed. Scalar field theories are defined using explicit
forms of derivative operators, traces and noncommutative frame fields for the
geometry, and various physical features are described. Noncommutative
worldvolume field theories of D-branes in the pp-wave background are also
constructed.
