Group completion via the action ∞-category

We give a generalization of Quillen's S⁻¹S construction for arbitrary Eₙ-monoids as an Eₙ₋₁-monoidal ∞-category and show that its realization models the group completion provided that n ≥ 2. We will also show how this construction is related to a variety of other constructions of the group completion.