The Greek verb apodechomai means to receive with acceptance or warm welcome — to welcome someone or to gladly accept something offered. It is stronger than simply 'to receive,' implying active, positive reception.
Apodechomai marks moments of genuine, enthusiastic reception in Acts. When Paul and Barnabas reported on their missionary journey, the Jerusalem church 'welcomed' (apodechomai) the news (Acts 15:4). Cornelius 'welcomed' Peter warmly (Acts 10:33, implied). Most significantly, in Acts 28:30, Paul 'welcomed' all who visited him during his Roman imprisonment — a model of open-armed hospitality even in chains. The word describes the posture God calls his people to: not guarded acceptance but joyful, wholehearted welcome of God's messengers and God's word.