Millennials are the most digitally connected generation to date, and where e-commerce is concerned, they may also be the most global.

New research from payments processor PayPal, conducted between September and October of last year, finds that millennials -- defined as those between the ages of 18 and 34 -- are more likely to shop across borders, regardless of the currency exchange rate or language. Ipsos, a research firm based in Paris, surveyed more than 23,000 online shoppers in 29 countries on behalf of PayPal.

Nearly half (48 percent) of millennials report being generally comfortable making a foreign purchase. Unsurprisingly, they're also more likely to do so on a smartphone; twenty percent say they'd made a cross-border purchase on their phone within the last year.

Small business owners are wise to focus on the massive potential of millennial shoppers, who are expected to spend as much as $1.4 trillion annually by 2020, according to  Accenture. That figure would represent 30 percent of all retail sales. Still, attracting those consumers is not necessarily an easy task.

The PayPal data suggests that millennials are savvy about their web purchases, and are thus influenced by benefits such as fast delivery, secure payment systems, promotions and discounts, and free shipping. The reported top factors for influencing a purchase are free shipping (51 percent of respondents) and faster delivery (40 percent of respondents.)

Across borders -- and especially in the U.S. and China -- it's worth noting that millennials shell out primarily for clothing, entertainment, electronics, and travel.

And e-commerce retailers might want to re-examine their return policies: Savvy millennials also aren't afraid to send an item back.