** Shares of National Storage REIT NSR.AX rise as much as 2.9% to hit a lifetime peak of A$2.81
** Self-storage operator signs scheme implementation deed with a consortium backed by Brookefield Asset Management and Singapore's GIC
** Takeover offer values co at A$4 billion ($2.65 billion)
** Co says board to back deal in the absence of a superior proposal
** More than 12.7 million shares change hands vs 30-day avg volume of around 10.9 million shares
** Stock up 19.9% YTD, including the day's moves
($1 = 1.5067 Australian dollars)
(Reporting by Nikita Maria Jino in Bengaluru)
((Nikita.Jino@thomsonreuters.com;))