Equivariant Grothendieck ring of a complete symmetric variety of minimal rank

We describe the $G$-equivariant Grothendieck ring of a regular compactification $X$ of an adjoint symmetric space $G\mathrm{/}H$ of minimal rank. This extends the results of Brion and Joshua for the equivariant Chow ring of wonderful symmetric varieties of minimal rank and generalizes the results by the author on the regular compactification of an adjoint semisimple group.