  Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with
$\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant
vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action.
We construct an equivariant K-theory of such quantum vector bundles using
Quillen's exact categories, and provide means for its compution. The
equivariant K-groups of quantum homogeneous spaces and quantum symmetric
algebras of classical type are computed.
