  We propose the operatorial form of Baxter's TQ-relations in a general form of
the operatorial B\"acklund flow describing the nesting process for the
inhomogeneous rational gl(K|M) quantum (super)spin chains with twisted periodic
boundary conditions. The full set of Q-operators and T-operators on all levels
of nesting is explicitly defined. The results are based on a generalization of
the identities among the group characters and their group co-derivatives with
respect to the twist matrix, found by one of the authors and P.Vieira
[V.Kazakov and P.Vieira, JHEP 0810 (2008) 050 [arXiv:0711.2470]]. Our
formalism, based on this new "master" identity, allows a systematic and rather
straightforward derivation of the whole set of nested Bethe ansatz equations
for the spectrum of quantum integrable spin chains, starting from the R-matrix.
