  Let $X$ be a smooth complex projective algebraic variety. Given a line bundle
$\mathcal{L}$ over $X$ and an integer $r>1$ one defines the stack
$\sqrt[r]{\mathcal{L}/X}$ of $r$-th roots of $\mathcal{L}$. Motivated by
Gromov-Witten theoretic questions, in this paper we analyze the structure of
moduli stacks of genus $0$ twisted stable maps to $\sqrt[r]{\mathcal{L}/X}$.
Our main results are explicit constructions of moduli stacks of genus $0$
twisted stable maps to $\sqrt[r]{\mathcal{L}/X}$ starting from moduli stack of
genus $0$ stable maps to $X$. As a consequence, we prove an exact formula
expressing genus $0$ Gromov-Witten invariants of $\sqrt[r]{\mathcal{L}/X}$ in
terms of those of $X$.
