  We obtain descriptions of central operator-valued Schur and Herz-Schur
multipliers, akin to a classical characterisation due to Grothendieck, that
reveals a close link between central (linear) multipliers and bilinear
multipliers into the trace class. Restricting to dynamical systems where a
locally compact group acts on itself by translation, we identify their
convolution multipliers as the right completely bounded multipliers, in the
sense of Junge-Neufang-Ruan, of a canonical quantum group associated with the
underlying group. We provide characterisations of contractive idempotent
operator-valued Schur and Herz-Schur multipliers. Exploiting the link between
Herz-Schur multipliers and multipliers on transformation groupoids, we provide
a combinatorial characterisation of groupoid multipliers that are contractive
and idempotent.
