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We construct well-behaved extensions of the motivic spectra representinggeneralized motivic cohomology and connective Balmer--Witt K-theory (amongothers) to mixed characteristic Dedekind schemes on which 2 is invertible. As aconsequence we lift the fundamental fiber sequence of $\eta$-periodic motivicstable homotopy theory established in [arxiv:2005.06778] from fields toarbitrary base schemes, and use this to determine (among other things) the$\eta$-periodized algebraic symplectic and SL-cobordism groups of mixedcharacteristic Dedekind schemes containing 1/2.

$\eta$-periodic motivic stable homotopy theory over Dedekind domains