  We present a definition of {\em twisted motivic Chern classes} for singular
pairs $(X,\Delta)$ consisting of a singular space $X$ and a $\mathbb Q$-Cartier
divisor containing the singularities of $X$. The definition is a mixture of the
construction of motivic Chern classes previously defined by
Brasselet-Sch{\"u}rmann-Yokura with the construction of multiplier ideals. The
twisted motivic Chern classes are the limits of the elliptic classes defined by
Borisov-Libgober. We show that with a suitable choice of the divisor $\Delta$
the twisted motivic Chern classes satisfy the axioms of the stable envelopes in
the K-theory. Our construction is an extension of the results proven by the
first author for the fundamental slope.
