  We study the nonnegative part \bar{G_{>0}} of the De Concini-Procesi
compactification of a reductive algebraic group G, as defined by Lusztig. Using
positivity properties of the canonical basis and parametrization of flag
varieties, we will give an explicit description of \bar{G_{>0}}. This answers
the question of Lusztig in [L4]. We will also prove that \bar{G_{>0}} has a
cell decomposition which was conjectured by Lusztig.
