We develop the theory of twisted stable maps into a tame Artin stack
M
\mathcal {M}
. We show that the stacks
K
g
,
n
(
M
)
\mathcal {K}_{g,n}(\mathcal {M})
of twisted stable maps are algebraic, and proper and quasi-finite over the corresponding stacks
K
g
,
n
(
M
)
\mathcal {K}_{g,n}(M)
of stable maps of the coarse moduli space
M
M
of
M
\mathcal {M}
. In the special case where
M
=
B
G
\mathcal {M}=\mathcal {B}G
, the classifying stack of a linearly reductive group scheme
G
G
, we show that
K
g
,
n
(
B
G
)
→
M
¯
g
,
n
\mathcal {K}_{g,n}(\mathcal {B}G)\to \overline {\mathcal {M}}_{g,n}
is a flat morphism with local complete intersection fibers.