  We introduce \textit{Kaestner brackets}, a generalization of biquandle
brackets to the case of parity biquandles. This infinite set of quantum
enhancements of the biquandle counting invariant for oriented virtual knots and
links includes the classical quantum invariants, the quandle and biquandle
$2$-cocycle invariants and the classical biquandle brackets as special cases,
coinciding with them for oriented classical knots and links but defining
generally stronger invariants for oriented virtual knots and links. We provide
examples to illustrate the computation of the new invariant and to show that it
is stronger than the classical biquandle bracket invariant for virtual knots.
