The True Blood star "seemed very excited about showing Kate around his hometown," says a source

Credit: Stefan Soderstrom/Expressen/Scanpix/Sipa

It must be getting serious! Alexander Skarsgard brought girlfriend Kate Bosworth to his home country of Sweden, where the lovebirds have been getting cozy – and meeting his friends.

The True Blood hunk, 33, and the actress, 27, arrived in Stockholm Thursday and engaged in some PDA while sightseeing in the city.

“They spent the whole weekend hand-in-hand and Alex seemed very excited about showing Kate around his hometown,” says an eyewitness. “Alex proudly introduced Kate to his best friends and everyone seemed to love Kate.”

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The couple, who stayed in an apartment that belongs to the actor s famous dad, Stellan Skarsgard, went for an evening stroll on Saturday before meeting up with friends at the romantic restaurant Aarts.

“Kate seemed to enjoy hanging out with Alex’s friends. Everyone was polite and made sure to speak English to include Kate in their conversations,” says a restaurant guest. “Kate looked very in love and happy with Alex. The couple kissed at the table several times and, at one point, Kate massaged his neck gently.”

On Sunday, Skarsgard and Bosworth seemed to be done with socializing: They picked up groceries at a local supermarket and made dinner at home.