Nobba means 'to reject', 'to refuse' or 'to say no to' someone or something, for example alla har ju blivit nobbad någon gång (everyone has been rejected at some point).
Another English translation would be 'snub' or 'to give the cold shoulder to'; it really depends on the context, because nobba can be a neutral rejection but can also imply a deliberate brush-off.
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Nobba has existed in Swedish for several years, originally mostly in the sense of a romantic rejection, but is now used to talk about everything from people turning down job offers to politicians ignoring their rivals' proposals.
Because it can be quite expressive, you'll often see in newspaper headlines. For example, the headline Grekland nobbar svenska turister (Greece rejects/snubs Swedish tourists) might accompany an article about Greece choosing to impose extra entry requirements on travellers from Sweden during the coronavirus crisis.
You can also use the phrase få nobben to mean 'to get rejected', for example föreslaget fick nobben av politikerna (the proposal was rejected by the politicians). Watch out, this only exists as a set phrase, so the noun nobb doesn't exist on its own in Swedish.
This is one of several words that found their way into the Swedish language via Romani, one of five minority languages spoken in Sweden. Nobba is a Swedified version of the Romani phrase no ba.
Hockeyspelaren nobbade utlandska lag för att stannar i Sverige
The hockey player rejected foreign teams to stay in Sweden
Skådespelaren blev nobbad på många provspelningar
The actress was rejected at many auditions