  We use \cite{G} to study the algebra structure of twisted cotriangular Hopf
algebras ${}_J\mathcal{O}(G)_{J}$, where $J$ is a Hopf $2$-cocycle for a
connected nilpotent algebraic group $G$ over $\mathbb{C}$. In particular, we
show that ${}_J\mathcal{O}(G)_{J}$ is an affine Noetherian domain with
Gelfand-Kirillov dimension $\dim(G)$, and that if $G$ is unipotent and $J$ is
supported on $G$, then ${}_J\mathcal{O}(G)_{J}\cong U(\g)$ as algebras, where
$\g={\rm Lie}(G)$. We also determine the finite dimensional irreducible
representations of ${}_J\mathcal{O}(G)_{J}$, by analyzing twisted function
algebras on $(H,H)$-double cosets of the support $H\subset G$ of $J$. Finally,
we work out several examples to illustrate our results.
