That sentence seems very clunky in English since you would never say "She has a sweater on (someone else)".
It can be helpful to remember the literal construction of the sentence, but sometimes you can't translate a phrase literally from one language to another, you have to translate its meaning.
Yes, Ireland was invaded by the Vikings. The Vikings established the cities of Dublin, Limerick, and Waterford. The population of Iceland's mitochondrial DNA is 50% Celtic, though these numbers might be confounded by the fact that people of Nordic descent had been settling and going native in Britain and Ireland long before Iceland was settled, so yeah, there was a lot contact between Ireland and Scandinavia in the Viking era.
Thank you for the information. How can Icelandic DNA be 50% Celtic. I know there's been a lot of debate about the definition of Celtic, but it is generally considered today (by the academic community - not all) that Celtic refers to language, so it wouldn't mean much to say Celtic DNA. Do you mean from the British Isles?
50% of mitochondrial DNA is of Celtic origin. 'Celtic' here doesn't just refer to the languages, but of the populations who are traditionally speakers of those languages, who do form distinct populations (note the plural) within the larger European population. Mind you, the borders are fuzzy, and even within those populations, there's local variation. It's very interesting to see what those variations are as they can tell us about how populations have migrated over time. You're right that the term 'Celtic' isn't a great one because the present day populations of Britain and Ireland were established long before the peoples who brought the Celtic languages and culture arrived, so it's something of a misnomer, but there's no decent alternative.
The thing about mitochondrial DNA is that it's essentially cloned from the mother (natural mutations from duplication withstanding), so it's super useful for tracing somebody's maternal lineage. What we find in Iceland is that the mitochondrial DNA of half the population of Iceland shares distinctive markers with populations in Scotland, Ireland, Northumbria, and, to a lesser extent, Wales.
Here's an interesting article on the genetic variation within Britain and Ireland: http://www.bbc.com/news/science-environment-31905764
Also, you might want to avoid using the term 'British Isles', especially around Irish people.
British Isles is the correct way of referring to both Britain and Ireland, even though Ireland is not part of Britain. I don't know why this is. The Celtic peoples covered vast areas of Europe as far as Turkey, although the main areas were what is now present day France, Switzerland, Belgium, Germany and Austria, so your mention of parts of Britain would only account for a percentage of the Celtic speaking peoples. That's why I wondered if you were meaning British and Irish rather than Celtic.
These things are not mutually exclusive. Also, people of Scandinavian descent are largely concentrated to Limerick, Dublin, and the South East (Wexford and Waterford), with very little influence outside of those areas. Similar patterns are repeated in Scotland and northern England. Abductions largely seem to have occurred on Ireland's northern and western coasts, and Scotland's west coasts.
They invaded, but that doesn't necessarily mean there was a huge influx of population. They largely just established a town to act as a trading hub.