An environmental organization with a $350 million war chest, a giant protest vessel, 28 activists and a rubber raft have succeeded in drawing Russian President Vladimir V. Putin into a very public global dispute. Attention is now focused on the Greenpeace activists who were arrested last month by Coast Guard agents for trying to hang a protest banner on an Arctic Ocean oil platform and whether they will languish in prison for up to 15 years each on dubious piracy charges.