  There are multiple conjectures relating the cohomological Hall algebras
(CoHAs) of certain substacks of the moduli stack of representations of a quiver
$Q$ to the Yangian $Y^{Q}_{MO}$ by Maulik-Okounkov, whose construction is based
on the notion of stable envelopes of Nakajima varieties. In this article, we
introduce the cohomological Hall algebra of the moduli stack of framed
representations of a quiver $Q$ (framed CoHA) and we show that the equivariant
cohomology of the disjoint union of the Nakajima varieties
$\mathcal{M}_Q(\text{v},\text{w})$ for all dimension vectors $\text{v}$ and
framing vectors $\text{w}$ has a canonical structure of subalgebra of the
framed CoHA. Restricted to this subalgebra, the algebra multiplication is
identified with the stable envelope map. As a corollary, we deduce an explicit
inductive formula to compute stable envelopes in terms of tautological classes.
