The Kerov-Kirillov-Reshetikhin (KKR) bijection is the crux in proving
fermionic formulas. It is defined by a combinatorial algorithm on rigged
configurations and highest paths. We reformulate the KKR bijection as a vertex
operator by purely using combinatorial R in crystal base theory. The result is
viewed as a nested Bethe ansatz at q=0 as well as the direct and the inverse
scattering (Gel'fand-Levitan) map in the associated soliton cellular automaton.Comment: 28 page