We report on subarcsecond observations of complex organic molecules (COMs) in the high-mass protostar IRAS 20126+4104 with the Plateau de Bure Interferometer in its most extended configurations. In addition to the simple molecules SO, HNCO and H₂¹³CO, we detect emission from CH₃CN, CH₃OH, HCOOH, HCOOCH₃, CH₃OCH₃, CH₃CH₂CN, CH₃COCH₃, NH₂CN, and (CH₂OH)₂. SO and HNCO present a X-shaped morphology consistent with tracing the outflow cavity walls. Most of the COMs have their peak emission at the putative position of the protostar, but also show an extension towards the south(east), coinciding with an H₂ knot from the jet at about 800-1000 au from the protostar. This is especially clear in the case of H_2¹³CO and CH₃OCH₃. We fitted the spectra at representative positions for the disc and the outflow, and found that the abundances of most COMs are comparable at both positions, suggesting that COMs are enhanced in shocks as a result of the passage of the outflow. By coupling a parametric shock model to a large gas-grain chemical network including COMs, we find that the observed COMs should survive in the gas phase for ˜2000 yr, comparable to the shock lifetime estimated from the water masers at the outflow position. Overall, our data indicate that COMs in IRAS 20126+4104 may arise not only from the disc, but also from dense and hot regions associated with the outflow.