Equivariant Cobordism of Smooth Projective Spherical Varieties

We study the equivariant cobordism rings for the action of a torus T on smooth varieties over an algebraically closed field of characteristic zero. We prove a theorem describing the rational T-equivariant cobordism rings of smooth projective G-spherical varieties with the action of a maximal torus T of G. As an application, we obtain explicit presentations for the rational equivariant cobordism rings of smooth projective horospherical varieties of Picard number one.