  For any algebraic scheme $X$ and every $(n,\mathscr{L})\in \mathbb{Z}\times
\text{Pic}(X)$ we define an associated involution of its Chow group $A_*X$, and
show that certain characteristic classes of (possibly singular) hypersurfaces
in a smooth variety are interchanged via these involutions. For
$X=\mathbb{P}^N$ we show that such involutions are induced by involutive
correspondences.
