  Building up on work of Epstein, May and Drury, we define and investigate the
mod $p$ Steenrod operations on the de Rham cohomology of smooth algebraic
stacks over a field of characteristic $p>0$. We then compute the action of the
operations on the de Rham cohomology of classifying stacks for finite groups,
connected reductive groups for which $p$ is not a torsion prime, and (special)
orthogonal groups when $p=2$.
