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The authors theoretically investigate quantum confinement and transition energies in quantum wells (QWs) asymmetrically positioned in wrinkled nanomembranes. Calculations reveal that the wrinkle profile induces both blue- and redshifts, depending on the lateral position of the QW probed. Relevant radiative transitions include the ground state of the electron (hole) and excited states of the hole (electron). Energy shifts as well as stretchability of the structure are studied as a function of wrinkle amplitude and period. Large tunable bandwidths of up to 70 nm are predicted for highly asymmetric, wrinkled QWs.