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Let $p$ be a prime number and $q=p^m$, with $m \geq 1$ if $p \neq 2,3$ and$m>1$ otherwise. Let $\Omega$ be any non-trivial twist for the complex groupalgebra of $\mathbf{PSL}_2(q)$ arising from a $2$-cocycle on an abeliansubgroup of $\mathbf{PSL}_2(q)$. We show that the twisted Hopf algebra$(\mathbb{C} \mathbf{PSL}_2(q))_{\Omega}$ does not admit a Hopf order over anynumber ring. The same conclusion is proved for the Suzuki groups, and for$\mathbf{SL}_3(p)$ when the twist stems from an abelian $p$-subgroup. Thissupplies new families of complex semisimple (and simple) Hopf algebras that donot admit a Hopf order over any number ring. The strategy of the proof isformulated in a general framework that includes the finite simple groups of Lietype.  As an application, we combine our results with two theorems of Thompson andBarry and Ward on minimal simple groups to establish that for any finitenon-abelian simple group $G$ there is a twist $\Omega$ for $\mathbb{C} G$,arising from a $2$-cocycle on an abelian subgroup of $G$, such that$(\mathbb{C} G)_{\Omega}$ does not admit a Hopf order over any number ring.This partially answers in the negative a question posed by Meir and the secondauthor.

Non-existence of integral Hopf orders for twists of several simple groups of Lie type