Base change functors in the {$\Bbb A\sp 1$}-stable homotopy category

Abstract

We relate base change functors of sheaves in ${\mathbb A}^1$-homotopy theory to group change functors from equivariant homotopy theory, and use these functors to construct elements of the Picard group of the ${\mathbb A}^1$-stable homotopy category. We also prove an analogue of the Wirthmüller isomorphism from equivariant homotopy theory in the ${\mathbb A}^1$-context.