PROVIDENCE, R.I. — Construction may begin this summer on an extended-stay hotel on a vacant, triangular lot in Providence's Capital Center Commission district because the Rhode Island Commerce Corporation agreed Monday night to give the developer as much as $4.8 million in taxpayer assistance over 20 years.The Commerce agency's board of directors unanimously approved the incentive for a Homewood Suites by Hilton, with 120 suites at 5 Exchange St.