  We construct a smooth Banach manifold BV$([a,b], M)$ whose elements are
suitably-defined functions $f:[a,b] \rightarrow M$ of bounded variation with
values in a smooth Banach manifold $M$ which admits a local addition. If the
target manifold is a Banach-Lie group $G$, with Lie algebra $\mathfrak{g}$, we
obtain a Banach-Lie group BV$([a,b], G)$ with Lie algebra BV$([a, b],
\mathfrak{g})$. Strengthening known regularity properties of Banach-Lie groups,
we construct a smooth evolution map from a Banach space of
$\mathfrak{g}$-valued vector measures on $[0,1]$ to BV$([0,1],G)$.
