  We study the Bochner-Riesz problem for the twisted Laplacian $\mathcal L$ on
$\mathbb R^2$. For $p\in [1, \infty]\setminus\{2\}$, it has been conjectured
that the Bochner-Riesz means $S_\lambda^\delta(\mathcal L) f$ of order $\delta$
converges in $L^p$ for every $f\in L^p$ if and only if $\delta>
\max(0,|(p-2)/p|-1/2)$. We prove the conjecture by obtaining uniform $L^p$
bounds on $S_\lambda^\delta(\mathcal L)$ up to the sharp summability indices.
