  We consider an open spin chain model with GL(N) bulk symmetry that is broken
to GL(M) x GL(N-M) by the boundary, which is a generalization of a model
arising in string/gauge theory. We prove the integrability of this model by
constructing the corresponding commuting transfer matrix. This construction
uses operator-valued "projected" K-matrices. We solve this model for general
values of N and M using the nested algebraic Bethe ansatz approach, despite the
fact that the K-matrices are not diagonal. The key to obtaining this solution
is an identity based on a certain factorization property of the reduced
K-matrices into products of R-matrices. Numerical evidence suggests that the
solution is complete.
