  In this article, we provide a detailed account of a construction sketched by
Kashiwara in an unpublished manuscript concerning generalized HKR isomorphisms
for smooth analytic cycles whose conormal exact sequence splits. It enables us,
among other applications, to solve a problem raised recently by Arinkin and
C\u{a}ld\u{a}raru about uniqueness of such HKR isomorphisms in the case of the
diagonal injection. Using this construction, we also associate with any smooth
analytic cycle endowed with an infinitesimal retraction a cycle class which is
an obstruction for the cycle to be the vanishing locus of a transverse section
of a holomorphic vector bundle.
