The Mumbai attacks have been linked to Lashkar-e-Taiba and radical Islamic groups in Kashmir generally. Saudi Arabia has contributed very much to what Lashkar-e-Taiba looks like, how it thinks, its motivation, ideology, and funding.
The notion of global Islam has also penetrated to Gaza and exists under the umbrella of Hamas. Hamas could agree to ahudna (calm) for fifty years, but there will be no recognition of Israel or a cessation of the struggle against it. If Hamas was ready to act pragmatically, it would no longer be Hamas.