Anna Melnikov provided a parametrization of Borel orbits in the affine variety square-zero n×n matrices by set involutions symmetric group. A related combinatorics leads to construction Bott-Samelson type resolution orbit closures. This allows compute cohomological and K-theoretic invariants orbits: fundamental classes, Chern-Schwartz-MacPherson classes motivic Chern torus-equivariant theories....