A bivariant functor is defined on a category of *-algebras and a category of
operator ideals, both with actions of a second countable group G, into the
category of abelian monoids. The element of the bivariant functor will be
G-equivariant extensions of a *-algebra by an operator ideal under a suitable
equivalence relation. The functor is related with the ordinary Ext-functor
for C∗-algebras defined by Brown-Douglas-Fillmore. Invertibility in this
monoid is studied and characterized in terms of Toeplitz operators with
abstract symbol.Comment: 12 page
