We introduce a new algebraic framework based on a modification (called exotic) of aromatic Butcher-series for the systematic study of the accuracy of numerical integrators for the invariant measure of a class of ergodic stochastic differential equations (SDEs) with additive noise. The proposed analysis covers Runge–Kutta type schemes including the cases of partitioned methods and postprocessed methods. We also show that the introduced exotic aromatic B-series satisfy an isometric equivariance property.