Theta groups over extensions of abelian varieties by unipotent groups

Let $0\to K_U\overset i\to Y\overset\pi\to X\to 0$ be a sequence of morphisms of algebraic groups over an algebraically closed field $k$, where $X$ is an abelian variety, $K_U$ is a unipotent, connected and commutative group scheme, and $(X,\pi)$ is a geometric quotient of $Y$ by $K_U$.
If $\mathcal L$ is an invertible sheaf over $X$, in this paper we generalize to $\overline{\mathcal L}=\pi^*\mathcal L$ the notion of a theta group associated with an invertible sheaf given by $D$. Mumford for an abelian variety.