This will be a report on a joint work in progress with Mina Aganagic.
Our goal is to produce an elliptic generalization of the stable
envelopes in K-theory (which will be briefly reviewed).
Elliptic stable envelopes depend on
an additional parameter $z$ in the complexification of Pic(X).
Elliptic stable envelopes limit to K-theoretic stable envelopes
with slope $s$ as the elliptic curve degenerates and
the Kahler/dynamical parameter $z$ goes
to infinity so that the ratio $z/\tau$ has a finite limit $s$.
Application awaiting such elliptic generalization include:
(1) geometric construction of elliptic R-matrices,
(2) monodromy of the K-theoretic quantum difference equation,
(3) precise correspondence of boundary conditions in dual 3-dimensional
susy gauge theories, and others.