Learn Icelandic: Bankinn er til hægri. - The bank is to the right.

In Icelandic, the definite article ('the') is added as a suffix to the end of the noun instead of being a separate word before it. Banki is a masculine word, so it takes the ending -inn to become bankinn (the bank).

The preposition til usually forces the following word into the genitive case. Why doesn't hægri change its ending here?

The words for 'right' (hægri) and 'left' (vinstri) are special adjectives in Icelandic because they are indeclinable. This means they never change their endings, regardless of case, gender, or what preposition comes before them.

If I want to say the bank is 'on the right' instead of 'to the right', can I still use til hægri?

No, til hægri specifically refers to direction ('to the right'). If you want to say something is located 'on the right side', you would use the phrase hægra megin.