I'm starting a website, that is meant for a non-English region, using an alphabet that is a bit different than that of English. Current plan is as follows. The website name, and the domain name, will be in the local language (not English); however, domain name will be spelled in the English alphabet, while the website's title will be the same word(s), but spelled properly with accents. E.g.: 'www.litterat.fr' and 'Littérat'.

Does the difference between domain name and website name character use influence the site's SEO? Is it better, SEO-wise, to choose a name that can be spelled the same way in the English alphabet? From my experience, when searching online, invariably, the English alphabet is used, no matter the language, so people will still be searching 'litterat' (without accents and such).

Edit:

To sum up:

Things have been said about IDN (Internationalized domain name). To make it simple, they are second-level domain names that contain language specific characters (LSP)(e.g. www.café.fr). Here you can check what top-level domains support what LSPs. Check initall's answer for more info on using LSPs in paths and queries.

To answer my question about how and if search engines relate keywords spelled with and without language specific characters: Google can potentially tell that series and séries is the same keyword. However, (most relevant for words that are spelled differently across languages and have different meanings, like séries), for Google to make the connection (or lack thereof) between e and é, it has to deduce two things:

1. Language that you are searching in. Language of your query. You can specify it manually through Advanced search or it guesses it, sometimes. I presume it can guess it wrong too. The more keywords specific to this language you use the higher Google's chance to guess the language.

2. Language of the crawled document, against which the ASCII version of the word will be compared (in this example – series). Again, check initall's answer for how to help Google in understanding what language your document is in.

Once it has that it can tell whether or not these two spellings should be treated as the same keyword. Google has to understand that even though you're not using french (in this example) specific characters, you're searching in French.

The reason why I used the french word séries in this example, is that it demonstrates this very well. You have it in French and you have it in English without the accent. So if your search query is ambiguous like our series, unless Google has something more to go on, it will presume that there's no correlation between your search and séries in French documents. If you augment your query to series romantiques (try it), Google will understand that you're searching in French and among your results you'll see séries as well. But this does not always work, you should test it out with your keywords first. For example, if you search series francaises, it will associate francaises with françaises, but it will not associate series with séries. It depends on the words.

Note: worth stressing that this problem is very relevant to words that, written in plain ASCII, might have some other meanings in other languages, it is less relevant to words that can be, by a distinct margin, just some one language.

Tip: I've noticed that sometimes even if my non-accented search query doesn't get associated with the properly spelled word in a document (especially if it's the title or an important keyword in the doc), it still comes up. I followed the link, did a Ctrl-F search for my non-accented search query and found nothing, then checked the meta-tags in the source and you had the page's title in both accented and non-accented forms. So if you have meta-tags that can be spelled with language specific characters and without, put in both.

Footnote: I hope this helps. If you have anything to add or correct, go ahead.