We consider the (twisted) warped Virasoro group Diff(S1)???? C∞(S1) in the presence of its three cocycles. We compute the Kirillov-Kostant-Souriau symplectic 2-form on coadjoint orbits. We then construct the Euclidean action of the ‘warped Schwarzian theory’ associated to the orbit with SL(2,R)×U(1) stabilizer as the effective theory of the reparametrization over the base circle and evaluate the corresponding one-loop-exact path integral. We further discuss thermodynamics of the wSch theory in comparison with the complex SYK model.

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