The Pegasus Asgard were motivated by a difference of opinion over the Asgard's clone research – something they knew was of existential importance to their survival. Reproduction by cloning had, over the course of many millennia, resulted in the Asgard's inability to reproduce sexually. Because the cloning technology was imperfect, the law of diminishing returns made it painfully apparent that their great race would one day go extinct.
When the Asgard leadership put ethical limitations on their scientists' research, one group determined to defy them and continue their work unrestricted. To keep their work secret they traveled by ship to the Pegasus Galaxy, arriving during war between the Ancients and the Wraith. With both powers occupied they believed they would be free to carry on their experiments ... but then the Wraith won the war, driving the Ancients from the city of Atlantis and back to the Milky Way.
Because the Wraith do not tolerate other advanced civilizations competing with them, the Asgard colony soon found itself under attack. Their intergalactic ships were destroyed in the first battle, leaving the Asgard trapped in the Pegasus Galaxy. They abandoned their settlements and retreated to a planet with a toxic atmosphere, where the Wraith could not and would not go, surviving only with the aid of their advanced environmental suits.
The colony was able to survive there for a time, but eventually the planet's environment became too harsh to tolerate. The Asgard were forced to venture back out into the galaxy, when they discovered an abandoned Ancient laboratory on M6H-987. Here they found the Attero project, evidently built by the scientist Janus as part of the war effort against the Wraith. When the Attero device is activated, Wraith ships anywhere in the galaxy will be destroyed whenever they attempt to enter hyperspace.
When Rodney McKay and Daniel Jackson found Janus' secret lab hidden inside Atlantis, the key to the Attero device was inadvertently activated. The Asgard were able to track it, infiltrate the city, and steal it – activating the device and potentially solving their Wraith problem, though at great cost to the rest of the galaxy. They were unconcerned that, as an unintended side effect, Janus' device also causes Stargates to explode when they are dialed.
Despite being cut off from the rest of the Asgard, their advanced technologies are many and impressive. In addition to being resistant to toxins, electricity, and bullets their suits have built-in energy shields, and enable the wearer to withstand a fall from a great height. The rogue Asgard also possess fast-moving fighter craft, with the ability to travel through hyperspace and to pass through Ancient shields unimpeded.
With the Attero device shut down, the Asgard retreated from the planet. The splinter group is still at large in the Pegasus Galaxy.
Note: The rogue Asgard have been nicknamed by fans as the "Vanir," after a race of gods in Norse mythology. Their name does not appear in any canon source.
FIRST APPEARED: The Lost Tribe
First Contact - When McKay and Jackson find Janus' lab the Asgard assault Atlantis, taking the key to activate the Attero device.
The Lost Tribe - The rogue Asgard reveal themselves to Daniel Jackson, and later fail in destroying the Wraith with the Attero device.