  For any scheme $M$ with a perfect obstruction theory, Jiang and Thomas
associate a scheme $N$ with symmetric perfect obstruction theory. The scheme
$N$ is a cone over $M$ given by the dual of the obstruction sheaf of $M$, and
contains $M$ as its zero section. Locally $N$ is the critical locus of a
regular function.
  In this note we prove that $N$ is a $d$-critical scheme in the sense of
Joyce. By assuming an orientation on $N$ there exists a global motive for $N$
locally given by the motive of vanishing cycles of the local regular function.
We prove a motivic localization formula under the good and circle compact
$\C^*$-action for $N$. When taking Euler characteristic the weighted Euler
characteristic of $N$ weighted by the Behrend function is the signed Euler
characteristic of $M$ by motivic method.
  As applications we calculate the motivic generating series of the motivic
Vafa-Witten invariants for K3 surfaces. This motivic series gives the result of
the $\chi_y$-genus for Vafa-Witten invariants of K3 surfaces, which is the same
(at instanton branch) as the K-theoretical Vafa-Witten invariants of Thomas.
