  Whenever a given Poisson manifold is equipped with discrete symmetries the
corresponding algebra of invariant functions or the algebra of functions
twisted by the symmetry group can have new deformations, which are not captured
by Kontsevich Formality. We consider the simplest example of this situation:
$\mathbb{R}^2$ with the reflection symmetry $\mathbb{Z}_2$. The usual
quantization leads to the Weyl algebra. While Weyl algebra is rigid, the
algebra of even or twisted by $\mathbb{Z}_2$ functions has one more
deformation, which was identified by Wigner and is related to Feigin's
$gl_\lambda$ and to fuzzy sphere. With the help of homological perturbation
theory we obtain explicit formula for the deformed product, the first order of
which can be extracted from Shoikhet-Tsygan-Kontsevich formality.
