  We study the equivariant cobordism theory of schemes for torus actions. We
give the explicit relation between the equivariant and the ordinary cobordism
of schemes with torus action. We deduce analogous results for action of
arbitrary connected linear algebraic groups. We prove some structure theorems
for the equivariant and ordinary cobordism of schemes with torus action and
derive important consequences. We establish the localization theorems in this
setting. These are used to describe the structure of the ordinary cobordism
ring of certain smooth projective varieties.
