Indigenous Group

The ethnic groups in Iceland are homogeneous rather than indigenous. Their descendants consist of Scandinavians and Norse, which made up 94% of the entire population. There are not really any specific group of indigenous people in Iceland and the following are several quotes from different sources to back the statement.
https://www.cia.gov/library/publications/the-world-factbook/geos/ic.html


http://www.arcticcentre.org/?DeptID=7768
(Click on the image, right click on the image, select "View Image", click on the image once to enlarge it)
The picture above is very useful to illustrate the various indigenous groups around the Artic regions. Iceland is not included as it does not have an indigenous group of people.

"Arctic indigenous peoples include for example Saami in circumpolar areas of Finland, Sweden, Norway and Northwest Russia, Nenets, Khanty, Evenk and Chukchi in Russia, Aleut, Yupik and Inuit (Iñupiat) in Alaska, Inuit (Inuvialuit) in Canada and Inuit (Kalaallit) in Greenland. All of the above-mentioned countries except Iceland have indigenous peoples living within their Arctic territory."
http://www.arcticcentre.org/?DeptID=7768

"Indigenous people - we don't have them in Iceland actually, but you would have in the (unintelligible) polar north the Inuit, or what used to be called the Eskimos. The Sami, or what used to be called the Lapps in Scandinavia and a number of other groups in Russian north and the American north."

This website also explains about the rights of indigenous people and impacts of climate change in the region
http://www.npr.org/templates/story/story.php?storyId=18690185

"Iceland and Greenland in the north were reached by Scandinavian sailors sometime around the year 1000."
http://www.wisegeek.com/which-islands-lack-an-indigenous-population.htm

"Among Icelanders the discourse on issues of the indigenous or aboriginal or First Nation people of the North is marked by the fact that Iceland does not have an indigenous population – that is, in the meaningful salient sense of the concept indigenous."
http://www.svs.is/JHI_PresentationCanadianGGroundtable.pdf

The Norse (Vikings) and the Scandinavians makes up the entire population of Iceland. Very much similar to that of its descendants, Scandinavia is filled with arts and culture. Architectures include concert halls, museums, culture houses filled the streets of Scandinavia.
http://visitscandinavia.com.au/DestinationsAndAttractions/Scandinavia.1/ArtsCulture.5.aspx