For a chosen dg model O0 of the Swiss Cheese operad, Alg(O0)_A is equivalent to Alg(E2^O)/Hoch(A), giving (Hoch(A), A) as a chain-level final action.
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Twisted tensor product of dg categories and Kontsevich's Swiss Cheese conjecture
For a chosen dg model O0 of the Swiss Cheese operad, Alg(O0)_A is equivalent to Alg(E2^O)/Hoch(A), giving (Hoch(A), A) as a chain-level final action.