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In this paper we establish the sharp asymptotic decay of positive solutionsof the Yamabe type equation $\frlap u=u^{\frac{Q+2s}{Q-2s}}$ in a homogeneousLie group, where $\frlap$ represents a suitable pseudodifferential operatormodelled on a class of nonlocal operators arising in conformal CR geometry.

Optimal decay for solutions of nonlocal semilinear equations with critical exponent in homogeneous group