  In this paper we address several algebraic constructions in the context of
groupoids, algebroids and $\mathbb Z$-graded manifolds. We generalize the
results of integration of $\mathbb N$-graded Lie algebras to the honest
$\mathbb Z$-graded case and provide some examples of application of the
technique based on Harish-Chandra pairs. We extend the construction to the
algebroids setting, the main example being the action Lie algebroid.
