Quantum Kirwan map and quantum Steenrod operation

We construct an equivariant extension of the quantum Kirwan map and show that it intertwines the classical Steenrod operation on the cohomology of a classifying space with the quantum Steenrod operation of a monotone symplectic reduction. This provides a new method of computing quantum Steenrod operations developed by Seidel-Wilkins. When specialized to the non-equivariant piece, our result also resolves the monotone case of Salamon's quantum Kirwan map conjecture in the symplectic setting.