Extended affine Weyl groups and Frobenius manifolds

We define certain extensions of affine Weyl groups (distinct from these considered by K. Saito [S1] in the theory of extended affine root systems), prove an analogue of Chevalley Theorem For their invariants, and construct a Frobenius structure on their orbit spaces. This produces solutions F(t(1),...,t(n)) of WDVV equations of associativity polynomial in t(1),..., t(n-1), exp t(n).