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Given a $C_\infty$ coalgebra $C_*$, a strict dg Hopf algebra $H_*$, and atwisting cochain $\tau:C_* \rightarrow H_*$ such that $Im(\tau) \subsetPrim(H_*)$, we describe a procedure for obtaining an $A_\infty$ coalgebra on$C_* \otimes H_*$. This is an extension of Brown's work on twisted tensorproducts. We apply this procedure to obtain an $A_\infty$ coalgebra model ofthe chains on the free loop space $LM$ based on the $C_\infty$ coalgebrastructure of $H_*(M)$ induced by the diagonal map $M \rightarrow M \times M$and the Hopf algebra model of the based loop space given by $T(H_*(M)[-1])$.When $C_*$ has cyclic $C_\infty$ coalgebra structure, we describe an $A_\infty$algebra on $C_* \otimes H_*$. This is used to give an explicit (non-minimal)$A_\infty$ algebra model of the string topology loop product. Finally, wediscuss a representation of the loop product in principal $G$-bundles.

Homotopy Algebra Structures on Twisted Tensor Products and String Topology Operations