  We analyze the linear conductance of a semiconductor quantum wire containing
a region where a local Rashba spin-orbit interaction is present. We show that
Fano lineshapes appear in the conductance due to the formation of quasi bound
states which interfere with the direct transmission along the wire, a mechanism
that we term the Fano-Rashba effect. We obtain the numerical solution of the
full Schr\"odinger equation using the quantum-transmitting-boundary method. The
theoretical analysis is performed using the coupled-channel model, finding an
analytical solution by ansatz. The complete numerical solution of the
coupled-channel equations is also discussed, showing the validity of the ansatz
approach.
