  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 $t_1, ..., t_{n-1}, \exp
t_n$.
