  Let $F$ be a global field. Let $G$ be a non trivial finite \'etale tame
$F$-group scheme. We define height functions on the set of $G$-torsors over
$F,$ which generalize the usual heights such as discriminant. As an analogue of
the Malle conjecture for group schemes, we formulate a conjecture on the
asymptotic behavior of the number of $G$-torsors over $F$ of bounded height.
This is a special case of our more general Stacky Batyrev-Manin conjecture from
arXiv:2207.03645. The conjectured asymptotic is proven for the case $G$ is
commutative. When $F$ is a number field, the leading constant is expressed as a
product of certain arithmetic invariants of $G$ and a volume of a space
attached to $G$. Moreover, an equidistribution property of $G$-torsors in the
space is established.
