Abstract
Recently the first two authors (Cattaneo and Felder in 2008) constructed an L ∞-morphism using the S 1-equivariant version of the Poisson Sigma Model. Its role in the deformation quantization was not entirely clear. We give here a “good” interpretation and show that the resulting formality statement is equivalent to formality on cyclic chains as conjectured by Tsygan and proved recently by several authors (Dolgushev et al. in 2008; Willwacher in 2008).