© 2016 Author(s). We study the optical properties of coaxial GaAs/InxGa1-xAs core/multishell nanowires with x between 0.2 and 0.4 at 10 K. The evolution of the photoluminescence energy of the InxGa1-xAs quantum well shell with x and shell thickness agrees with the result of 8-band k·p calculations, demonstrating that the shell growth is pseudomorphic. At low excitation power, the photoluminescence from the shell is dominated by the recombination of exciton states deeply localized within the shell. We show that these states are associated with crystal-phase quantum rings that form at polytype segments of the InxGa1-xAs quantum well shell.