  For a twisted $C^*$-dynamical system $(\mathscr{A},\mathbb{R}^n,\alpha,e)$
over a unital $C^*$-algebra we establish a weakly parametric pseudodifferential
calculus analogously to the celebrated weakly parametric calculus due to Grubb
and Seeley. If the $C^*$-algebra $\mathscr{A}$ has an $\alpha$-invariant trace
then we prove an expansion of the resolvent trace (with respect to the dual
trace on multipliers) for suitable pseudodifferential multipliers. The question
whether the expansion holds true as a Hilbert space trace expansion in concrete
GNS spaces for $\mathscr{A}$ will be addressed in a future publication.
