Cancellation theorem for framed motives of algebraic varieties

The machinery of framed (pre)sheaves was developed by Voevodsky [17]. Based on the theory, framed motives of algebraic varieties are introduced and studied in [5]. An analog of Voevodsky?s Cancellation Theorem [18] is proved in this paper for framed motives stating that a natural map of framed S1-spectra Mfr(X)(n) _+ Hom(G,Mfr(X)(n+ 1)), n 0, is a schemewise stable equivalence, where Mfr(X)(n) is the nth twisted framed motive of X. This result is also necessary for the proof of the main theorem of [5] computing fibrant resolutions of suspension P1-spectra ??P1 X+ with X a smooth algebraic variety. The Cancellation Theorem for framed motives is reduced to the Cancellation Theorem for linear framed motives stating that the natural map of complexes of abelian groups