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Let [X/G] be a smooth Deligne-Mumford quotient stack. In a previous paper theauthors constructed a class of exotic products called inertial products onK(I[X/G]), the Grothendieck group of vector bundles on the inertia stackI[X/G]. In this paper we develop a theory of Chern classes and compatible poweroperations for inertial products. When G is diagonalizable these give rise toan augmented $\lambda$-ring structure on inertial K-theory.  One well-known inertial product is the virtual product. Our results show thatfor toric Deligne-Mumford stacks there is a $\lambda$-ring structure oninertial K-theory. As an example, we compute the $\lambda$-ring structure onthe virtual K-theory of the weighted projective lines P(1,2) and P(1,3). Weprove that after tensoring with C, the augmentation completion of this$\lambda$-ring is isomorphic as a $\lambda$-ring to the classical K-theory ofthe crepant resolutions of singularities of the coarse moduli spaces of thecotangent bundles $T^*P(1,2)$ and $T^*P(1,3)$, respectively. We interpret thisas a manifestation of mirror symmetry in the spirit of the Hyper-KaehlerResolution Conjecture.

Chern Classes and Compatible Power Operations in Inertial K-theory