  In previous articles, a magnetic pseudodifferential calculus and a family of
C*-algebras associated with twisted dynamical systems were introduced and the
connections between them have been established. We extend this formalism to
symbol classes of H\"ormander type with an x-behavior modelized by an abelian
C*-algebra. Some of these classes generate C*-algebras associated with the
twisted dynamical system. We show the relevance of these classes to the
spectral analysis of pseudodifferential operators with anisotropic symbols and
magnetic fields.
