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We explain our previous results about Hochschild actions [Kau07a, Kau08a]pertaining in particular to the coproduct which appeared in a different form in[GH09] and provide a fresh look at the results. We recall the general action,specialize to the aforementioned coproduct and prove that the assumption ofcommutativity, made for convenience in [Kau08a], is not needed. We givedetailed background material on loop spaces, Hochschild complexes anddualizations, and discuss details and extensions of these techniques which workfor all operations of [Kau07a, Kau08a].  With respect to loop spaces, we show that the co--product is well definedmodulo constant loops and going one step further that in the case of a gradedGorenstein Frobenius algebra, the co--product is well defined on the reducednormalized Hochschild complex.  We discuss several other aspects such as ``time reversal'' duality andseveral homotopies of operations induced by it. This provides a cohomologyoperation which is a homotopy of the anti--symmetrization of the coproduct. Theobstruction again vanishes on the reduced normalized Hochschild complex if theFrobenius algebra is graded Gorenstein.  Further structures such as ``animation'' and the BV structure and a coloringfor operations on chains and cochains and a Gerstenhaber double bracket arebriefly treated.

A detailed look on actions on Hochschild complexes especially the degree $1$ co-product and actions on loop spaces